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sid.inpe.br/mtc-m21b/2016/02.04.22.21-TDI
HIGH ENERGY EMISSIONS FROMTHUNDERSTORMS:HEETS, FROM PHOTONS TO
NEUTRONS TOWARD THE GROUND
Gabriel Sousa Diniz
Master’s Dissertation of theGraduate Course in SpaceGeophysics, guided by Drs.Fernanda de São Sabbas Tavares,and Ute Maria Ebert, approved inmarch 04, 2016.
URL of the original document:<http://urlib.net/8JMKD3MGP3W34P/3L56P52>
INPESão José dos Campos
2016
PUBLISHED BY:
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sid.inpe.br/mtc-m21b/2016/02.04.22.21-TDI
HIGH ENERGY EMISSIONS FROMTHUNDERSTORMS:HEETS, FROM PHOTONS TO
NEUTRONS TOWARD THE GROUND
Gabriel Sousa Diniz
Master’s Dissertation of theGraduate Course in SpaceGeophysics, guided by Drs.Fernanda de São Sabbas Tavares,and Ute Maria Ebert, approved inmarch 04, 2016.
URL of the original document:<http://urlib.net/8JMKD3MGP3W34P/3L56P52>
INPESão José dos Campos
2016
Cataloging in Publication Data
Diniz, Gabriel Sousa.D615h High energy emissions from thunderstorms:HEETs, from
photons to neutrons toward the ground / Gabriel Sousa Diniz.– São José dos Campos : INPE, 2016.
xxiv + 103 p. ; (sid.inpe.br/mtc-m21b/2016/02.04.22.21-TDI)
Dissertation (Master in Space Geophysics) – Instituto Nacionalde Pesquisas Espaciais, São José dos Campos, 2016.
Guiding : Drs. Fernanda de São Sabbas Tavares, and Ute MariaEbert.
1. Neutrons. 2. Photons. 3. Cross sections. 4. Monte Carlo.I.Title.
CDU 550.385.4
Esta obra foi licenciada sob uma Licença Creative Commons Atribuição-NãoComercial 3.0 NãoAdaptada.
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 UnportedLicense.
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“Corri como um louco em busca da felicidade e trouxe apenas as mãos vazias
pendentes de ilusões. Caminhei então, devagar, em busca do meu próprio
destino e hoje trago as mãos cheias carregadas de vida.”
Illusion’s wanderer - Ildegardo Rosa / Emmanuel Mirdad (2014)
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A meus pais, coautores de todos meus bons sucessos. E a minha avó Zefinha,
matriarca de toda uma família.
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ACKNOWLEDGMENTS
First of all, I thank my parents João França and Maria Lúcia for all the support
and comprehension that they always kindly gave to me.
I thank my supervisors, Dra. Fernanda São Sabbas for the orientations and
financial support that she provided me for my trips. And Dra. Ute Ebert also for
the orientations, her comments enhanced the potential of what I was capable to
do, and for the financial support during my travels through the project 10757
“Understanding Lighting” of the Netherlands’ Foundation for Technological
Research (STW).
A special thanks to my friend Casper Rujtes, PhD student of the project
12PR3041-2 “Cosmic Lightning” of the Netherlands’ Foundation for
Fundamental Research of Matter (FOM). Casper comments, advices and
guidance during my work helped me greatly. Working with him was a pleasure
and a lesson.
In particular, I would like to thanks my friends who came from Brasília with me.
Adam Smith, Lorena do Carmo and Matheus Gross, our friendship and their
support kept me sane in the darkest hours during this period.
I thank my partner, Cínthia Stecchini, for all the care and comprehension in the
final part of this work that she gave me.
Thanks to all my friends, colleges and professors from the spatial geophysics
and astrophysics INPE department. Without them, working and living in São
José dos Campos would be a totally different experience and thanks to them, it
was a lovely one.
Thanks to all my friends and colleges from the CWI, for the lovely reception and
moments that they provided me during my work abroad.
I thank Dra. Maria Virginia Alves and Régia Pereira for the support during my
weak moments.
To my dear friends that entered at INPE together with me, Marcos Grala and
José Paulo Marchezi, my thanks. Sharing all this period with them was really
special to me.
I would like to thanks my friend Dr. Ivan Soares for all the incentive that he
provided me so I could continue with this work.
To all my dear ones that I left in Brasília, without their cheer I would not be able
to complete my tasks.
x
I thank my friend, Gabriel Rübinger-Betti, for the conversations, advices and
support that he gave me. May there be more vinyl and whysky evenings.
I thank CAPES and CNPq for the financial support through all my work that
gave me the opportunity of reaching this point.
I thank the FAPESP project LEONA, grant 2012/20366-7, for the support.
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ABSTRACT
Thunderstorms are the starting point of several intense phenomena such as
gamma rays and X rays, neutron, positron and electron emissions. The X rays
and gamma rays have energies that may reach 100 MeV. The neutron
emissions may be created by energetic gamma ray photons interacting with the
air via Giant Dipole Resonance, a photonuclear reaction, related to
thunderstorms and lightning in a way that is not completely understood yet. In
this work neutrons were assumed to be created by gamma ray photons in the
energy range of 10-30 MeV emitted by leader discharges. Their production and
propagation toward the ground were investigated using computer simulations.
Cross sections data banks were analyzed to provide estimations on the
neutrons creation probability. The analysis revealed that the probability per
collision of a photonuclear occurs varies between 0 and 3.2% through the
energy range of 10 and 30 MeV. The photons mean free path within this energy
range was analyzed together with the atmospheric density profile showing that
for photon source altitudes above 1 km, the photons with this energy pass
through a sufficiently high number of mean free path to ensure a collision. The
free software EGS5 was used to treat the photons and electrons motion through
the atmosphere in the intent of analyze the spread of the beams, that were
assumed to be monodirectional. The photon beam presented an aperture of 2-
6º ± 2° while the electron beam was broader showing an aperture of 11-13º ±
3°. Since EGS5 does not take into account neutron production and motion, the
neutron analysis was done with the FLUKA software simulating a photon beam
in different initial heights and estimating the photon and neutron ground
detection. FLUKA simulations have shown that neutrons are distributed at the
ground within a radius of 2 km away from the source axis. The neutrons
reached ground with a rate of 10-4-10-2 neutrons per gamma, which agrees with
the cross section analysis done upon the neutron production. The neutron
number decrease was used to estimate an upper limit of 5 km for the altitude of
a punctual photon source that is capable of generating ground detectable
neutrons.
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EMISSÕES DE ALTA ENERGIA PROVINDAS DE NUVENS DE
TEMPESTADE. HEETS: DE FÓTONS PARA NÊUTRONS AO SOLO
RESUMO
Nuvens de tempestade são o início de vários fenômenos intensos como os
raios gama e raios X, bem como de emissões de nêutrons, pósitrons e elétrons.
As emissões de raios X e raios gama possuem energias que alcançam 100
MeV. As emissões de nêutrons podem ser criadas por interações entre raios
gamma com o ar através da Ressonância Gigante de Dipolo, uma reação foto-
nuclear, relacionadas com as nuvens de tempestade e com raios de um modo
ainda não totalmente compreendido. Neste trabalho supõe-se que os nêutrons
são criados por fótons de raios gamma com energia entre 10-30 MeV emitidos
durante a propagação do líder negativo. A produção e a propagação pelo ar
destes nêutrons foram investigadas utilizando simulações computacionais.
Bancos de dados de seções de choque foram analisados para estimar a
probabilidade por colisão de uma reação foto-nuclear acontecer. A análise
revelou que essa probabilidade varia entre 0% e 3.2% para fótons com energia
entre 10 e 30 MeV. O livre caminho médio dos fótons no intervalo de energia
de 10-30 MeV foi analisado junto com o perfil de densidade atmosférica. A
análise mostrou que para fótons com altitude inicial acima de 1 km, eles
passam por livres caminhos médios o suficiente para a probabilidade de
ocorrência de ao menos uma colisão ser garantida. O software livre EGS5
baseado no método Monte Carlo foi usado para tratar o movimento dos fótons
e elétrons pela atmosfera no intuito de estudar a difusão de feixes
monodirecionais dessas partículas. Foi observado que o feixe de fótons possui
uma abertura entre 2-6º ± 2° enquanto o feixe de elétrons possui uma abertura
de 11-13º ± 3°. A análise de nêutrons foi feita com o software FLUKA
simulando um feixe de fótons em diferentes altitudes iniciais e estimando a
detecção de fótons e nêutrons no solo. As simulações do FLUKA mostraram
que os nêutrons se distribuem no solo em uma distância radial da fonte de 2
km, chegando ao solo numa razão entre 10-4 até 10-2 nêutrons/fótons, o que
concorda com a análise das seções de choque. A diminuição dos nêutrons
detectados em solo permitiu a estimativa de uma altura limite de 5 km para
uma fonte pontual de fótons capaz de produzir nêutrons detectáveis em solo.
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FIGURE LIST
Pág.
2.1 - Illustration of Compton effect and the scattering angle. Source: Brehm et al., 1989............................................................................................................ 11 2.2 - Pair production and bremsstrahlung emission Feynman diagrams. Source: Hirayama et al. (2005). ..................................................................................... 12 2.3 - Photonuclear reaction cross section in air components. .......................... 14 2.4 - Generation of bremsstrahlung photons Source: Haug et al., 2004. .......... 15 2.5 - Geometric representation of the bremsstrahlung process. Source: Köhn, 2014. ................................................................................................................ 16 2.6 - Example of TGFs detected by BATSE. Source: Fishman et al. (1994).. .. 19 2.7 - Position of RHESSI satellite during the TGF measurements. The upper panel shows the RHESSI’s position over the expected distribution of the observed TGFs if they were evenly distributed over the globe. The scale is a fraction of maximum exposure. The lower panel shows RHESSI’s position over the long-term lightning frequency data, with the scale in flashes per squared kilometer per year. Source: Smith et al. (2005). ............................................... 20 2.8 - TGF cumulative count spectrum, background–subtracted, of the 130 TGFs measured by AGILE. The dashed curve represents a pre-AGILE
phenomenological model (F(E)~ E−αe−E EC⁄ ) with α = 4.0 ± 0.2 and EC = 6.6 ±1.2 MeV, while the solid curve is the broken power-law fit. Source: Tavani et al. (2011).. ............................................................................................................. 22 2.9 - Dose enhancement during thunderstorm measured by ERMs. Source: Torii et al. (2002). ............................................................................................. 24 2.10 - Calculated photon spectra on the ground with different electric fields. Source: Torii et al.(2002).. ............................................................................... 25 2.11 - Rate between the neutron and positron production and rate between the proton and positron production as function of the photon energy. Source: Köhn (2014). .............................................................................................................. 31 2.12 – Neutron energy distribution after 14 μs of the simulation start. Source: Köhn (2014). ..................................................................................................... 31 3.1 - Upper panel, OTD lightning map. Middle panel, Mir's neutron flux measurements. Lower panel, Kolibri measurements. Source: Bratolyubova-Tsulukidze et al. (2004).. .................................................................................. 35 3.2 - Neutron count versus electric field strength in the presence of lightning discharges in July 26, 2010. The straight line represents the count rate before the thunderstorm. Source: Starodubtsev et al. (2012). ..................................... 37 3.3 - Record of neutron counting rate and the local electric field. Source: Gurevich et al. (2012).. ..................................................................................... 38 3.4 - Simulated neutron spectrum using GEANT4. Source: Chilingarian et al. (2012b). ............................................................................................................ 41 3.5 - Neutron burst and lightning correlation. The first panel shows the neutron count and the second panel shows the electric field variations in temporal coincidence with the neutron detection. Source: Toropov et al. (2013).. .......... 42 3.6 - Energy neutron spectra on 30 km altitude (continuous line), and on 500 km (dashed line). Source: Malyshkin et al. (2010)………………………………..44 3.7 - Simulated neutron energy spectrum on the source altitude. Source: Babich et al.(2010)……………………………………………………………… ......45
xvi
3.8 - (a) Simulated neutron energy spectra. The black line is at the moment of neutron's creation, the black dots are the neutrons reaching the ground and the gray line are the ones reaching satellite altitudes. (b) Dispersion of simulated neutrons in a 20 degree aperture cone, in gray, and isotropically, in black. Source: Carlson et al. (2010b). ......................................................................... 47 3.9 - Simulated neutron energy spectrum. Source: Drozdov et al. (2013). ....... 48 4.1 - Cross sections of the dominant photon interactions with dry air. Cs (blue) is Compton scattering; Pp is pair production; Pn is photoneutron reaction and Pnp is photoproton reaction. ............................................................................. 52 4.2 – Compton scattering for EGS5, GEANT4 and Köhn (2014) ...................... 55 4.3 - Pair production cross section for EGS5, GEANT4 and Köhn (2014). ....... 55 4.4 - Probability per collision of primary photons to produce neutrons via photoneutron reaction as the rate between the photoneutron cross section and the total photon cross section. .......................................................................... 57 4.5 - Normalized probability of neutron production plotted against the incident photon energy Eγ, minus the bound energy Eb.. .............................................. 58 4.6 - Probability of neutron production by photons with energies above 30 MeV accounting for Compton scattering as first interaction and subsequent neutron production by the secondary photon. ............................................................... 58 4.7 - Probability of neutron creation as a function of photon energy. ................ 59 5.1 - Photon mean free path averaged in energy. Range 1: 10-15 MeV; Range 2: 15-20 MeV; Range 3: 20-25 MeV and Range 4: 25-30 MeV. ....................... 62 5.2 - The number of mean free paths as a function of source altitude, χt
represents the photons χ considering the total cross section; and Ni is the integrated density. ............................................................................................ 64 6.1 - Average photon beam aperture as a function of the altitude of the initial beam. ............................................................................................................... 70 6.2 - Average electron beam aperture as function of initial beam altitude. ....... 71 6.3 - Number of photons reaching the ground from a photon beam as function of initial beam altitude. ...................................................................................... 71 6.4 - Number of photons reaching the ground from an electron beam as function of initial beams altitude. ...................................................................... 72 7.1 - Top view of simulation geometry .............................................................. 75 7.2 - Photons down to 50 keV per primary photon (between 10 and 30 MeV) on ground as function of source altitude. The inset is a zoom view of the altitude region 2-5 km. .................................................................................................. 76 7.3 - Neutrons per primary photon on ground as function of source altitude. The inset is a zoom view of the altitude region 2-5 km. ........................................... 77 7.4 - Total photon at the ground with different source heights. ......................... 78 7.5 - Total neutron spectra at the ground with different source heights.. .......... 79 7.6 - Photon energy spectra for different detectors with source altitude of 2 km ......................................................................................................................... 80 7.7 - Photon energy spectra for different detectors with source altitude of 0.3 km. ................................................................................................................... 81 7.8 - Neutron energy spectra for different detectors with source altitude of 2 km and 0.3 km ........................................................................................................ 82 7.9 - Photons per primary photon recorded by different detectors at different radial distances from the source axis. The different colors represent the four distinct simulations with different initial photon energy range. .......................... 84
xvii
7.10 - Neutrons per primary photon recorded by different detectors at different radial distances from the source axis. The different colors represent the four distinct simulations with different initial photon energy range. .......................... 85
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TABLE LIST
Pág.
3.1 - Summary of Shyam et al.(1999) results……………………………………..34 3.2 - Observations and simulations results and characteristics summary. ....... 49 6.1 - Equivalence between distance z travelled at constant air density and the actual atmospheric altitude H. .......................................................................... 69 7.1 - Detector radii. ........................................................................................... 83 7.2 - Neutron detection according with the FLUKA simulations with the observation parameters……………………………………………………………..87 A.1 - GEANT4 Compton scattering parameters…………………………………102 A.2 - GEANT4 pair production parameters ..................................................... 103
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ABBREVIATION LIST
TLE Transient Luminous Event
TGF Terrestrial Gamma-ray Flash
BATSE Burst And Transient Source
Experiment
CGRO Compton Gamma-Ray Observatory
HEET High Energy Emissions from
Thunderstorm
RREA Relativistic Run-away Electron
Avalanche
LMA Lightning Mapping Array
UAD Upward Atmospheric Discharges
IC Intra-Cloud
CG Cloud-to-Ground
GC Ground-to-Cloud
STP Standard Temperature and Pressure
OTD Optical Transient Detector
LIS Lightning Imaging Sensor
TRMM Tropical Rainfall Measurement
Mission
RHESSI Reuven Ramaty High Energy Solar
Spectroscope Imager
SAA South Atlantic Anomaly
LAT Large Area Telescope
xxii
GBM Gamma-ray Burst Monitor
MCAL Mini-Calorimeter
ER Environmental Radiation
CR Cosmic Rays
ERMs Environmental Radiation Monitors
EGS4 Electron Gamma-ray Shower 4
EGS5 Electron Gamma-ray Shower 5
GROWTH Gamma-Ray Observation of Winter
Thunderclouds experiment
CORSIKA COsmic Ray SImulations for
KAscade
ASEC Aragats Space Environment Center
TGE Terrestrial Gamma-ray
Enhancements
MOS Modification Of energy Spectra
AGILE Astro‐Rivelatore Gamma a Immagini
Leggero
ISS International Space Station
APF Analyzer of Particles and Fields
SNT Solar-Neutron Telescope
YBJNM Yangbajing Neutron Monitors
ANM Aragats Neutron Monitor
GDR Giant Dipole Resonance
xxiii
SUMMARY
Pág.
1. Introduction. ................................................................................................. 1
2. High Energy Emissions from Thunderclouds. ........................................... 7
2.1. Mechanism of gamma ray and neutron production...................................... 8
2.1.1 Compton Scattering ................................................................................. 10
2.1.2 Pair production ........................................................................................ 12
2.1.3 Photonuclear reaction .............................................................................. 13
2.1.4 Bremsstrahlung emission ........................................................................ 15
2.2. Basic concepts about thunderclouds ......................................................... 16
2.3. Measurements of atmospheric gamma rays .............................................. 18
2.3.1. Ground detection of Gamma- rays ......................................................... 23
2.4. Simulations of gamma rays related with atmospheric processes .............. 28
3. Atmospheric neutrons ............................................................................... 33
3.1. Simulations of neutrons related with atmospheric processes .................... 43
4. On neutrons production probability ......................................................... 51
4.1. Cross section analysis results ................................................................... 56
5. Analysis of the particles mean free path .................................................. 61
5.1. Mean free path analysis results ................................................................. 63
6. Particle beams widening and EGS5 .......................................................... 67
6.1. Beam aperture results .............................................................................. 70
7. On FLUKA simulations .............................................................................. 73
7.1. Simulation results ...................................................................................... 76
8. Discussion and conclusions ..................................................................... 89
References ...................................................................................................... 93
A. Appendix- EGS5 and GEANT4 cross section equations .......................... 101
xxiv
1
1. Introduction.
Since the 80's a series of new phenomena resulting from thundercloud electrical
activity started to be reported in the literature. Some of these phenomena occur
at high altitudes, in the atmosphere above the clouds, and others make their
way to the ground. Franz et al. (1990) were the first group to document the
mesospheric plasma discharge that is now known as Sprite. This phenomenon
is part of a class of events that are collectively called Transient Luminous
Events (TLE), which are transient plasma events spanning from the
stratosphere, ~20 km altitude, to the bottom of the night-time ionosphere, at
~100 km altitude. The most well known TLEs are the Elves, Halos, Blue Jets,
Gigantic jets and the Sprites.
Five years before sprites were reported for the first time Shah et al. (1985)
reported observations of neutron emissions related to lightning, providing the
first indication that thunderclouds produce energetic emissions. In the same
year Alexeyenko et al. (1985) reported an augmentation on the count of
secondary cosmic ray emissions in the presence of a cumulus-nimbus cloud,
i.e. a thundercloud. And Fishman et. al (1994) first reported the phenomena
known now as Terrestrial Gamma-ray Flashes (TGFs), which are gamma ray
emissions from thundercloud electrical activity that correspond to
electromagnetic radiation in the MeV range of energy.
The TGFs were detected by the Burst And Transient Source Experiment
(BATSE), an instrument onboard the Compton Gamma-Ray Observatory
(CGRO) satellite. The discovery of TGFs marked the beginning of yet a new
science field that investigates High Energy Emissions from Thunderstorms
(HEETs). Since then, the data from several Astrophysical satellites have been
studied to look for TGFs, ground and airplane observations have been
performed to investigate these phenomena that remain mysterious in various
aspects.
The work proposed here is to study the neutron emissions related to lightning
discharges. It is the second work to be done in this field of research in South
America, the first being the work of Winkelman (2014) on possible detection of
2
HEET by the detectors of Pierre Auger Cosmic Ray Observatory in Argentina.
This is the first work about neutrons. Computer simulations will be used to
investigate gamma-ray and neutron emissions related to the thunderstorm
discharges reaching the ground. The hypothesis that will be used is that the
neutrons are generated via photonuclear reactions of gamma ray photons
emitted by negative lightning leaders. The neutron propagation to the ground
was simulated using Monte Carlo simulations.
The results of this work have the potential to contribute to increase the
comprehension of thunderstorm neutron emissions, and will provide a first
reference for future observations and computational studies. In particular it will
provide a reference to the ground based neutron observations that will be
performed using the sensors of the Transient Luminous Event and
Thunderstorm High Energy Emission Collaborative Network in Latin America,
LEONA network, which is an INPE ongoing project, currently funded by
FAPESP.
Two software packages for particle simulations were used, EGS5 and FLUKA,
to investigate the motion of electrons, photons and neutrons in the atmosphere
towards the ground. The atmosphere was assumed to be dry, and the air
composition was 78.085% Nitrogen, 20.950% Oxygen, and 0.965% Argon. The
simulations, data and results treatment were performed using the software
packages EGS5, FLUKA and MatLab.
EGS5 was used to analyze the motion of photon and electron beams, since the
electrons are the photon source, through an atmosphere at 1.2250x10-3 g/cm3
density. There was no electric field in these simulations because EGS5 does
not allow its implementation. The lack of electric field makes the electrons
diffuse isotropically. This isotropic emission is considered as an upper limit for
the electron diffusion since an upward directed electric field from a
thunderstorm would prevent further diffusion for the charged particles. It was not
used to simulate neutron emissions and their motion because it does not hold
the necessary photonuclear reaction and neutron transport in order to track
neutron motion in the atmosphere.
3
EGS5 is a Monte Carlo based program that allows the analysis of
electromagnetic particle showers. It is controlled by a user code with definitions
on the simulation mean, the particles initial condition and the output format. The
program tracks the motion of particles using statistical methods on the collision
criteria.
FLUKA was used to register the neutrons detection on the ground level. FLUKA
is also a Monte Carlo based program. It is design for general calculations of
particle transport and interaction with the matter that are not electromagnetic.
The program allows the user to determine arbitrary combinatory geometry,
different types of output format and input conditions.
MatLab is used to do all the statistical treatment on the raw data provided by
FLUKA and EGS5. It is also used to elaborate routines for the cross section and
mean free path analysis.
The neutrons produced via photonuclear reaction were then analyzed and
several important quantities were estimated:
The approximate altitude range of a point-like photon source that is
capable of generating ground detectable neutrons;
The neutron production per gamma photon based on cross section and
mean free path;
The maximum distance that the neutrons reached from the source axis;
The energy of the neutrons that reached the ground;
The aperture angle of the photon beam toward the ground, and of the
electron beam that generated this photon beam.
All results obtained in this work were compared with the ground observations
available in the literature.
Before simulating the photon propagation to the ground and generation of
neutrons along the way, the probability of a photonuclear reaction to occur was
estimated by comparing the photons total cross section with their photonuclear
reaction cross section. The second step was to perform a comparison between
4
the cross section of different software packages used in particle simulations.
The considered packages were EGS5, GEANT4 and the code recently written
by Christoph Köhn (2014). EGS5 and GEANT4 use analytical expressions for
Compton scattering and pair production cross sections while Köhn used
numerical expressions for those cross sections. The objective was to find out
how these packages agreed for Compton scattering and pair production cross
sections since both process are well-known theoretically.
Chapter 2 presents a general review of the basic concepts that involve the
phenomena. Rapid describing the mechanism of gamma ray and neutron
generation, then starting a description of the thundercloud where these events
begin, it is presented a review on the important particle processes for the
energy regime treated in this work (Sections 2.1.1-2.1.4), in further sections it is
presented a description of gamma ray emission events related with
thunderstorms. Chapter 3 presents the neutron participation on this set of
phenomena, in this chapter is found the measurements and simulations of
neutron emission related to thundercloud and lightning.
Chapter 4 presents a general cross section evaluation to have a first estimate of
the probability of a photonuclear reaction to happen among all the others
possible photon interactions in the HEETs energy range. The cross section data
allowed an estimate for the neutron spectrum at source altitude, and showed
the possibility of neutrons production by photons with energy higher than the
photonuclear reaction limits, involving other collisions in between. Different sets
of cross sections for the main interactions in this energy range were compared,
showing the variation on cross section values due to different programs
treatment to add confidence in the used expressions.
In chapter 5, an atmospheric exponential density profile is adopted to estimate
the number of mean free path a photon has from different initial altitudes toward
the ground. Differentiating the fraction of photons that are likely to engage into a
collision along the beams path.
Chapter 6 explains the implementation of the program Electron Gamma ray
Shower 5 (EGS5) used to simulate monodirected electron and photon beams,
5
and analyze the diffusion of these beams as they move through a constant
density medium without electric field.
In chapter 7, the FLUKA program was adopted to simulate monodirected
photon beams moving through an atmospheric density profile simulated by a
series of slabs with constant density, with different values, to approximate the
actual atmospheric density profile. The spectra of the particles at the ground for
a given initial photon spectrum was also calculated.
6
7
2. High Energy Emissions from Thunderclouds
Neutron emissions related to thunderstorms have been observed by space
borne instrumentation, such as the ones reported by Bratolyubova-Tsulukidze
et al. (2004), and by ground equipments, such as the ones reported by Torii et
al.(2002), Tsuchyia et al. (2011), Shah et al. (1985), Martin et al.(2010) and
Toropov et al.(2013). They have made clear that gamma ray photons and
neutron emissions related to thunderstorm and to lightning discharges are able
to reach great distances. Even though, more space and ground measurements
as well as theoretical development are necessary to improve the understanding
about such phenomena.
The effort of all observation and simulation studies have helped clarifying and
explaining several characteristics of High Energy Emissions from
Thunderstorms, but there are still plenty of unanswered questions to be
explored. The source of the neutron emissions and the mechanism of the
gamma ray emissions that generate the neutrons are still unknown, as well as
their effects on living organisms.
The main goal of this work was to study neutron production by thunderstorm
electrical activity via computer simulations. To do so, lightning discharges were
assumed to produce energetic electrons, which by their turn produce gamma
ray photons that create the neutron showers via photonuclear reactions. The
high energy emission occurs during the steps of lightning discharges negative
leader, since the leader’s electric field highest values are very concentrated in
the range of approximately 30 cm (KÖHN, 2014); the photon beam source can
be considered as punctual. During the simulations, monodirectional beams are
considered because there is no relevant interaction between beams in different
direction that would make the problem nonlinear. In particular, the beams in this
study are always directed to the ground because of the main interest is in
particle ground detection.
The means by which lightning produces energetic electrons and gamma rays is
the subject of several papers in the literatures, such as Köhn 2014; Celestin et
al. (2012), and is beyond the scope of this dissertation. The photon energy
8
range considered here was from 10 to 100 MeV in order to take into account the
lowest energy photon capable of producing a neutron and the highest energy
measured up to date (TAVANI et al., 2011).
2.1. Mechanism of gamma ray and neutron production
The TGF generation mechanism is not well understood yet. The Relativistic
Runaway Electron Avalanche (RREA) mechanism has been used to model long
lasting TGFs. The Lightning Mapping Array (LMA) observations with satellite
have shown correlations between TGFs and negative lightning leaders
(CUMMER et al., 2005). Extending the RREA mechanism with feedback
process, the relativistic feedback model of TGFs, was presented by Dwyer
(2012). This model includes feedback effects from positrons and energetic
photons as the runaway electrons emit bremsstrahlung photons that may be
backscattered to the start of the avalanche region, starting a new avalanche
and resulting in a self-sustaining mechanism.
This research line has some precursor works such as Wilson (1925); Libby and
Lukens (1973). But the more constant and elaborated research it is recent,
since it effectively started in the mid 1980 – 1995 with works of Fishman et al.
(1994) and Shah et al. (1985). Both papers were received as novelty and
started giving a more consistent base for the following works. Since then, more
hypotheses about these phenomena have been developed.
The idea of neutron been produced by lightning discharges was first
hypothesized by Libby and Lukens (1973) and it was thought as a fusion
reaction involving deuterium occurring inside the lightning plasma channel. This
mechanism was soon discarded by a photonuclear reaction.
Babich et al. (2007) revisited mathematically these mechanisms and showed
that the fusion mechanism is impossible due to the lack of enough acceleration
for the deuterium ions to the threshold of the reaction and also because of the
small quantity of deuterium ions in the air. Even for electric fields 20-30 times
the conventional breakdown the neutron yield remains small in comparison to
9
the projections of Libby and Lukens (1973). Due to Babich et al. (2007), there is
now a strong believe in the photonuclear reactions mechanism, with the neutron
measurements it is clear that is needed a large number of photons exciding the
threshold of 10 MeV. Observations have shown spectra exciding 20 MeV.
Babich et al. (2007) showed a mechanism of Upward Atmospheric Discharges
(UADs), in which relativistic electrons are driven upward until altitudes where
they become magnetized by the geomagnetic field and drift horizontally
according to the ExB product defined by the geomagnetic field and the
thunderstorm electric field. This mechanism have a bremsstrahlung spectrum
extending beyond 20 MeV and with 1017 source electrons could produce
enough photons to be consistent with Fishman et al. (1994) gamma ray
measurements, reaching a resultant of 1015 neutrons produced by discharge. In
an estimation of neutrons reaching the detector in comparison to the experiment
of Shah et al. (1985), which was well above sea level at a height of 2.7 km, the
neutron flux produced by the UAD mechanism suffered significantly attenuation
with a result of 3x10-8 neutrons at the detector per discharge, showing that
neutrons from a point source at the stratosphere are not able to reach the
detector altitude.
Estimations from an intracloud discharge mechanism was also performed by
Babich et al. (2007) with gamma-ray data from Dwyer et al.(2004) giving a total
neutron per discharge of 4x1013 but at a height of 5.7 km.
Under the effect of thundercloud's electric field, high energy particles may gain
more energy from the electric field rather than lose energy in collisions and
accelerate, entering in a runaway regime (WILSON, 1925). RREA process
produces runaway electrons via hard elastic scattering of energetic electrons
with atomic electrons, resulting in an avalanche that increases exponentially
with the distance (DWYER et al., 2008).
As an avalanche process, it needs a seed particle, i.e., a high energy particle
that starts the process, which can be either from cosmic rays that enter the
Earth (BABICH et al., 2012) or atmospheric charged particles that are
10
accelerated in the electrical field at the head of lightning leaders (CARLSON et
al., 2010a).
The idea of correlating TGF with negative lightning leaders was proposed by
Moore et al. (2001) and used by Xu et al. (2012) and also by Köhn (2014).
According with this hypothesis, the gamma-ray producing electrons are not
accelerated by the thunderstorm electric field alone but they are initially
accelerated by the strong and inhomogeneous electric field near the lightning
leader head. This assumption allowed Celestin et al. (2012) to reach a
simulated spectrum that agree with the new high energy observations
performed by Tavani et al. (2011), which reach energies of 100 MeV. Köhn
(2014) had especially good results following this approach. He presented clear
particle production and propagation involving neutrons, protons and positrons.
Köhn (2014) analytically calculated bremsstrahlung cross-sections and was
able to show the gamma ray production during the step process with the
highlighted importance of electron-electron bremsstrahlung emission (KÖHN et
al., 2014) in the negative lightning leader.
Bremsstrahlung emissions are very important for this work, since they are
assumed to be the source of the gamma rays that generate the neutrons. The
following subsections will describe in more details Compton scattering and pair
production, which are the dominant interactions, and Bremsstrahlung
emissions.
2.1.1 Compton Scattering of photons
The issue of neutron production and TGFs deals with gamma ray photons with
energies up to 100 MeV (TAVANI et al., 2011). In this energy range the most
probable interaction between the photons and matter is the Compton Scattering
(HIRAYAMA et al., 2005). The photon has both energy (휀) and momentum (P)
which are related by Equation 2.1
휀 = ℎ𝜈 = 𝑃𝑐 =ℎ𝑐
𝜆 , (2.1)
where frequency is 𝜈, wavelength is 𝜆 and h being the Planck’s constant.
11
As it is scattered, the photon suffers an interaction and origin a photon with
different wavelength. This is a function of the scattering angle (BREHM et al.,
1989), as illustrate on Figure 2.1. Experimental results have shown that the
photon is scattered on the electron rather than on the atom itself, since there is
no difference in the process when different atomic targets are used. The
wavelength of the scattered photon is always longer than the incident, showing
that the photon looses energy during the collision.
Figure 2.1 - Illustration of Compton effect and the scattering angle.
Source: Brehm et al. (1989).
Compton scattering is then described as a relativistic collision between a photon
and an electron and the scattered wavelength can be found applying the
conservation laws of energy and total momentum. The elastic scattering
treatment can be done, without losing generality, setting the electron target
initially at rest. This way, the electron momentum ( 𝑷) will be the difference
between the incident (𝒑) and scattered (𝒑′) photon momentum (Equation 2.2)
𝒑 − 𝒑′ = 𝑷, (2.2)
The relation between the total particle energy and its momentum is represented
relativistically and involves the rest energy (Equation 2.3),
𝐸2 = (𝑃𝑐)2 + 𝑚2𝑐4, (2.3)
in which E is the total energy, m is the mass, and c is the speed of light.
Completing the set of Equations, the system energy conservation (Equation 2.4)
휀 + 𝑚𝑐2 = 휀 ′ + 𝐸 , (2.4)
12
where 휀 is the incident photon energy, 𝑚 is the electron mass, 휀 ′ is the emitted
photon energy and E is the total electron energy. These four Equations can be
manipulated to express the wavelength shift that occurs in the Compton effect
(Equation 2.5),
𝜆′ − 𝜆 =ℎ
𝑚𝑐(1 − cos 𝜃) , (2.5)
where 𝜆′ is the scattered photon’s wavelength and 𝜆 is the incident photon’s
wavelength and the angle 𝜃 is the scattering angle. The Equation 2.5 shows
that 𝜆′ is always larger than 𝜆 so the scattered photon is always less energetic.
2.1.2 Pair production of photons
The electron-positron pair production by the interaction of a photon with a
nucleus is a very similar process with the brehmsstrahlung emission. This can
be seen by the Feynman’s diagrams of each process in Figure 2.2. In both
cases the incident particle is scattered by two photons. In this representation,
the positron can be treated as an electron travelling backward in time. The
positron is scattered by two photons, the incident one and a virtual one from the
nucleus. The incident photon is then converted into an electron-positron pair
during the process.
Figure 2.2 - Pair production and bremsstrahlung emission Feynman diagrams. Source: Hirayama et al. (2005).
The incident photon’s energy is divided between the created electron and
positron. This energy is converted into the particle mass and kinetic energy.
13
The process is described by its cross section, Equation 2.6, which can be
obtained from the bremsstrahlung cross section by substituting the incident
electron for the produced positron and the emitted photon by the incident
photon from the nucleus (KÖHN, 2014).
𝑑4𝜎 =𝑍2𝛼𝑓𝑖𝑛𝑒
3𝑐2|𝑝+||𝑝−|𝑑𝐸+𝑑Ω+𝑑Ω−𝑑Φ
(2𝜋)2𝜔3|𝑞|4ℏ[−
𝑝−2 sin2 Θ−(4𝐸+
2−(𝑐𝑞)2)
(𝐸−−𝑐|𝑝−| cos Θ−)2 −
𝑝+
2 sin2 Θ+(4𝐸−2−(𝑐𝑞)2)
(𝐸+−𝑐|𝑝+| cos Θ+)2 +2ℎ2𝜔2(𝑝+
2 sin2 Θ++𝑝−2 sin2 Θ−)
(2𝜋)2(𝐸+−𝑐|𝑝+| cos Θ+)(𝐸−−𝑐|𝑝−| cos Θ−)−
2|𝑝+||𝑝−| sin Θ− sin Θ+ cos Φ(2𝐸−
2+ 2𝐸+2−(𝑐𝑞)2)
(𝐸+−𝑐|𝑝+| cos Θ+)(𝐸−−𝑐|𝑝−| cos Θ−)] , (2.6)
where 𝑝+ is the positron momentum, 𝑝− is the electron momentum; 𝑍 is the
target atom atomic number, 𝐸− is the electron total final energy and 𝐸+ is the
electron total initial energy. The virtual photon has a momentum 𝒒 and the
incident photon has a momentum k, Θ+ is the angle between k and 𝒑+ , as well
as Θ− is the angle between k and 𝒑− . Finally, the angle Φ is between the
planes determined by the two pair of vectors (k, 𝒑+) and (k, 𝒑−). The values
𝛼𝑓𝑖𝑛𝑒 and 𝜔 are the fine structure constant and the emitted photon angular
frequency respectively.
2.1.3 Photonuclear reactions of photons
The interactions between gamma ray photons and atomic nuclei due the strong
interaction are called photonuclear reactions. These processes occur in an
indirect manner as the gamma ray photons themselves are indifferent to the
strong force by nature. Gamma ray interacting with matter may produce pairs of
matter-antimatter (like electron positron pairs) for any elementary charged
particle (TAVERNIER, 2010). If the created particles exchange momentum and
energy with the nucleus, those reactions are possible.
The strong interactions of gamma rays are similar to the interactions of any
hadrons, but their cross sections are lower by a factor of 100. Below 10 MeV,
the photonuclear reactions are extremely small because of the mismatch
between the energy to create the virtual quark-antiquark pair and the energy
available in the gamma rays.
14
The reactions of interest are 𝑁714 (𝛾, 1𝑛) 𝑁7
13 , 𝑂816 (𝛾, 1𝑛) 𝑂8
15 and 𝐴𝑟1840 (𝛾, 1𝑛) 𝐴𝑟18
39 ,
which are the emissions of one neutron through the interaction between an
energetic gamma ray photon and these nuclei. Since the actual target on the
atmosphere are diatomic molecules of Nitrogen and Oxygen and the
monoatomic Argon gas, the microscopic molecular cross sections on Nitrogen
and Oxygen are the microscopic cross sections of respective elements
multiplied by two, representing the multiplicity of targets.
The cross sections may be compared in Figure 2.3. One can see that the Argon
cross section is larger but due to its small density in the atmosphere, the
majority of emitted neutrons are expected to come from a photonuclear reaction
with Nitrogen or Oxygen. The cross sections are in the energy range of a
process called Giant Dipole Resonance (GDR), i.e. 10-30 MeV, which is the
energy region where the nuclear particles, neutrons and protons, respond
resonantly to electromagnetic perturbations and may be emitted out of the atom
(CARLSON et al., 2010). The GDR does not have significant values above 30
MeV.
Figure 2.3 - Microscopic photonuclear reaction cross section of the considered
elements.
15
2.1.4 Bremsstrahlung emission of electrons
This process is characterized by the emission of a photon when an electron is
scattered by the nucleus of an atom (HAUG et al., 2004). As the electron
approaches the nucleus of the atom its direction changes, changing its velocity
and the speed may also be affected. The electron is actually “slowed down” in
the process and a photon is emitted with the energy released by the electron,
as illustrated in Figure 2.4. Bremsstrahlung is currently considered to be the
source of the high energy photons observed in association with thunderstorms
and individual lightning discharges.
Figure 2.4 - Generation of bremsstrahlung photons. Source: Haug et al. (2004).
The process is described through the triply differential cross section, carrying
the information about: (1) whether or not a collision takes place for a given
electron energy; (2) the photon energy and the angle between the incident
electron and the emitted photon; (3) the angle at which the electron is scattered.
The Equation 2.7 is a modify version of the Bethe and Heitler (BETHE et al.,
1934) cross section by (modified by Köhn (2014)):
𝑑4𝜎 =𝑍2𝛼𝑓𝑖𝑛𝑒
3ℎ2|𝑝𝑓|𝑑𝜔𝑑Ωi𝑑Ωf𝑑Φ
(2𝜋)4|𝑝𝑖|𝜔|𝑞|4 [𝑝𝑓
2 sin2 Θf(4𝐸𝑓2−(𝑐𝑞)2)
(𝐸𝑓−𝑐|𝑝𝑓| cos Θf)2 + 𝑝𝑖
2 sin2 Θi(4𝐸𝑓2−(𝑐𝑞)2)
(𝐸𝑖−𝑐|𝑝𝑖| cos Θi)2 +
2ℎ2𝜔2(𝑝𝑓2 sin2 Θf+𝑝𝑖
2 sin2 Θi)
(2𝜋)2(𝐸𝑓−𝑐|𝑝𝑓| cos Θf)(𝐸𝑖−𝑐|𝑝𝑖| cos Θi)−
2|𝑝𝑓||𝑝𝑖| sin Θi sin Θf cos Φ(2𝐸𝑖2+ 2𝐸𝑓
2−(𝑐𝑞)2)
(𝐸𝑓−𝑐|𝑝𝑓| cos Θf)(𝐸𝑖−𝑐|𝑝𝑖| cos Θi)] , (2.7)
where 𝑝𝑖 is the electron initial momentum, 𝑝𝑓 is the electron final momentum; 𝑍
is the target atom atomic number, 𝐸𝑓 is the electron total final energy and 𝐸𝑖 is
the electron total initial energy. The virtual photon exchanged between the
electron and the target atom has a momentum 𝒒 and the emitted photon has a
momentum k, Θi is the angle between k and 𝒑𝒊 , as well as Θf is the angle
16
between k and 𝒑𝒇 as illustrated by the Figure 2.5. Finally, the angle Φ is
between the planes determined by the two pair of vectors (k, 𝒑𝒊) and (k, 𝒑𝒇).
The values 𝛼𝑓𝑖𝑛𝑒 and 𝜔 are the fine structure constant and the emitted photon
angular frequency respectively.
Integrating this expression, Equation 2.7, it is possible to extract the total cross
section and the other differential cross sections.
Figure 2.5 - Geometric representation of the bremsstrahlung process. Source: Köhn, 2014.
2.2. Basic concepts about thunderclouds
The neutron emissions are one of the results of thunderstorm electrical activity.
Recent theories place the source of the short duration HEETs on the lightning
leaders (XU et al. 2012). However, there are some models that consider the
thunderstorm electric field themselves with the universal spectrum of relativistic
runaway electron avalanche bremsstrahlung as the photon source (BABICH et
al. 2010,).
Clouds are formed as soon as air parcels with enough humidity and with a
temperature that is higher than the surrounding atmosphere are transported
upwards to a cooler region, where the water vapor condensates. Thunderclouds
are clouds that have a large enough vertical development that the particles that
form them, water droplets and ice particles of different sizes, become electrified
through collisions while they are carried up and down by the updrafts and
downdrafts that take place inside the convective regions of these clouds. One
important condition for thunderstorm electrification is the simultaneous
17
existence of all three phases of water at what is called the mixed-phase region
(COORAY, 2014).
The meteorological conditions at the region where the clouds are formed
influence severely the thunderclouds characteristics. For example, the local
availability of water vapor influences the water quantity available to the
formation of the cloud. The level of atmospheric instability is important for the
initial cloud development, and the vertical winds influence how much cloud
mass can be sustained on the air. Cloud formation requires condensing nuclei
to gather water molecules, so aerosol concentration in the atmosphere may
also influence thunderclouds formation and electrification. For example, Lyons
et al. (1998) and São Sabbas et al. (2010) reported that large concentration of
aerosols coming from forest fires may be related to the development of
convective systems with strong positive electrification, leading to an increase of
positive cloud-to-ground lightning and consequent prolific production of
Transient Luminous Events (TLEs), especially sprites.
Thunderclouds are the clouds with the largest vertical development, they
normally reach the tropopause, region where there is an inflection point of the
temperature and it starts to increase with altitude. The tropopause height varies
considerably with latitude, being at 17 km at the tropics, 12-13 km at
midlatitudes summer and 6-7 km at midlatitudes winter (COORAY, 2014). For
gamma ray and neutron satellite observation, the cloud top height is an
important parameter because it can help determine the initial altitude at which
these particles are generated, since some theoretical works and measurements
consider negative lightning leaders reaching the cloud tops as the source of
these emissions.
TGFs are the most well studied of the HEETs, and current models of neutron
production have them as the triggers of the reactions that lead to neutron
emissions (KÖHN, 2014). On their turn, the current models explaining TGF are
placing their source in the lightning discharges. For example, one of the TGF
production mechanisms is based on bremsstrahlung emission that happens
during the lightning leader propagation phase (KÖHN, 2014). Therefore
18
understanding the characteristics of lightning discharges is important to
understand TGF production and the related neutron enhancements events.
Lightning are electrical discharges that may occur in the atmosphere every time
the electric field generated by the electrical charges inside a thundercloud
exceed the dielectric insulating capability of the air and electrical breakdown
takes place. However, recent studies have shown that the discharge may
initiate in sub-breakdown electric fields due to the time-scale of the electric field
changes and the dielectric response of ice particles inside the thundercloud
which does not respond rapidly enough to provide a greater obstacle for the
discharge formation (DUBINOVA, A. et al. 2015).The initial stages of lightning
discharges involve the construction of an ionized path for the electric current to
move through a plasma channel. An electrical structure called streamer is the
precursor to the electrical breakdown process. The streamer is a self
propagating discharge that ionizes the air due a high electric field while it
passes because of a high electric field on its head. It establishes a conductive
channel between the contact points of the discharge creating the path for the
leader propagation (KÖHN, 2014).
Leaders are visible large discharge channels that grow on a kilometer scale
(KÖHN, C. 2014). In particular, the negative lightning leader propagates itself in
steps in a not fully understood process that promotes the emission of energetic
radiation.
2.3. Measurements of atmospheric gamma rays
Terrestrial Gamma-Ray Flashes are the most well studied and therefore well
understood of the HEETs, such as positrons and neutrons emissions. They
were first reported by Fishman et al. (1994) with BATSE detectors onboard the
Compton Gamma-Ray Observatory (CGRO), a satellite launched in April of
1991. They were correlated with thunderstorm as there were thunderstorm
complexes below the satellite when it performed the measurements, leading
Fishman et al. (1994) to suggest that TGFs were caused by thunderstorm
electrical activity. Fishman et al. (1994) measured events with short duration,
0.1 - 2 ms, and with estimated gamma ray energy fluence on the order of 108 to
19
109 ergs, higher than other events found in nature (Figure 2.6). They considered
these events to be rare, since BATSE observed only 12 events in 2 years of
data, which gives a periodicity of less than once every two months.
As a matter of clarification, fluence is the amount of a quantity entering a certain
area defined as quantity per Area. Therefore, energy fluence have units of
[J/m2] in the MKS unit system. While flux is defined as fluence per time, as an
example, particle flux have units of [1/m2s] in the MKS unity system. Fishman et
al. (1994) refer to fluence in [ergs], referring actually to the energy deposited.
Figure 2.6 - Example of TGFs detected by BATSE. Source: Fishman et al. (1994).
Later on, Smith et al. (2005) reported the first six months of Reuven Ramaty
High Energy Solar Spectroscope Imager (RHESSI) satellite observations with
86 TGFs detected. RHESSI was designed to study x-ray and gamma-ray from
solar flares (Figure 2.7). It has a low altitude equatorial orbit, with 38 degrees. It
was launched in February of 2002 carrying Germanium detectors covering the
whole energy range from hard X-rays to gamma rays, from ~3 keV up to ~20
MeV, with a ~1cm thick Germanium planar detector in front of a ~7 cm thick
Germanium coaxial detector capable of measuring gamma rays with energies
up to 20 MeV. The estimated frequency of TGFs measured by RHESSI was of
20
10 to 20 TGFs per month. The duration of the observed events ranged from 0.2
to 3.5 ms and the total number of photons per event ranged from 17 to 101.
Figure 2.7 - Position of RHESSI satellite during the TGF measurements. The
upper panel shows the RHESSI’s position over the expected
distribution of the observed TGFs if they were evenly distributed
over the globe. The scale is a fraction of maximum exposure.
The lower panel shows RHESSI’s position over the long-term
lightning frequency data, with the scale in flashes per squared
kilometer per year.
Source: Smith et al. (2005).
The distribution of the events around the globe is apparently concentrated on
tropical latitudes. Comparing the TGF distribution with lightning maps, Smith et
al. (2005) found some notable points, as a lack of TGF in the southern US, a
region that has a high incidence of thunderstorm and lightning discharges, and
the highest density of TGF on central Africa, the region with the highest
lightning rate of the globe. There was no data from the South America Anomaly
SAA region where the spacecraft passes through Earth’s inner radiation belt.
Since the spectra consistently followed power laws with indices between -0.6
and -1.5, the emissions were interpreted by Smith et al. (2005) as
21
bremsstrahlung, with resulting electron energies on the order of 1 MeV or
higher. The bremsstrahlung emission model suggested that electrons with 20 to
40 MeV generated TGF photons. The coincidences between the TGF
distribution measured by RHESSI and the lightning maps reinforced the
connection between thunderstorms and TGF events.
The next set of satellite observations that brought significant new understanding
to TGFs were performed by the Fermi gamma-ray space telescope (BRIGGS et
al. 2010). It was launched in July 2008 and is orbiting the Earth at 565 km
altitude in an equatorial orbit with 25.58 degrees of inclination. Fermi consists of
two instruments designed to detect gamma rays, the Large Area Telescope
(LAT) and the Gamma-ray Burst Monitor (GBM). The former is a pair-
conversion telescope, which utilizes the generation of an electron-positron pair
in its detection, dedicated to the range of 20 MeV to more than 300 GeV while
the later has 12 NaI scintillators that cover the range of 8 keV - 1 MeV and two
Bismuth Germanate (BGO) scintillators covering the range of 200 keV – 40
MeV. Briggs et al. (2010) reported the TGF observations performed by GBM
that registered 12 TGF events on its first year of operation. Four of these TGFs
were specifically associated with lightning discharges detected by the World
Wide Lightning Location Network– WWLLN. Most photons had energies up to
30 MeV but there was a single measurement with 38 MeV. The peak flux
detected in their work was 3600 photons/cm2.s as an upper limit to their
measurements.
Some astonishing results were presented by Tavani et al. (2011), extending the
TGF spectrum to 100 MeV. The observations were performed by the Astro‐
Rivelatore Gamma a Immagini Leggero – AGILE space mission, which is
dedicated to gamma-ray measurements of astrophysical objects in the range of
30 MeV- 30 GeV. AGILE has been operating since April 2007 at an equatorial
orbit at 540 km altitude with inclination of 2.47 degrees, and is detecting an
average of 10 TGFs per month. The gamma–ray detector in this mission is a
pair-tracking telescope based on a tungsten-silicon tracker that operates in the
range of 30 MeV to 30 GeV, and a mini-calorimeter (MCAL) based on Csl(TI)
scintillating bars dedicated to the range of 300 keV to 100 MeV, with a
separated plastic anti-coincidence detector. The mini-calorimeter is triggered by
22
events with at least 10 photons and energy of 1.4 MeV. Observations with this
instrument confirmed Fermi measurements of TGFs with energies up to 40
MeV, plus registered a long tail in the TGF spectrum reaching energies up to
100 MeV, as shown in Figure 2.8.
Figure 2.8 - TGF cumulative count spectrum, background–subtracted, of the
130 TGFs measured by AGILE. The dashed curve represents a
pre-AGILE phenomenological model (𝐹(𝐸)~ 𝐸−𝛼𝑒−𝐸 𝐸𝐶⁄ ) with 𝛼 =
4.0 ± 0.2 and 𝐸𝐶 = 6.6 ± 1.2 MeV, while the solid curve is the
broken power-law fit.
Source: Tavani et al. (2011).
The new measurements performed by AGILE showed that the photons with
more than 10 MeV are approximately 10% of TGF energy spectra, therefore
TGFs span a higher energy range than initially expected. Since the
photoneutron cross-section has a lower bound of 10 MeV and peak at 20-30
MeV, Tavani et al. (2011) estimated that more than 1013 neutrons would be
created per TGF. Correlating the lightning data with TGF observations, Tavani
et al. (2011) reached the conclusion that the TGF distribution is not a random
sub-sample of global lightning activity as detected from space, i.e., the
distribution of TGF does not follow directly the lightning activity. They estimated
that the probability of the TGF distribution to be a sub-sample of lightning
distribution is 87% in Asia but only 3% in Africa.
23
2.3.1. Ground detection of Gamma- rays
The first ground record of particle emissions related with thunderclouds was
performed by Alexeyenko et al. (1985) who reported an augmentation of up to
1% on the count of secondary cosmic ray emissions correlated with electric field
perturbations. Starting in 1975 they recorded 140 events and ruled out
explanations related with variations of temperature and pressure. They
established a connection with the meteorological nature of the perturbation as
these events were more likely observed in the presence of cumulus-nimbus
clouds, i.e. thunderstorms.
The first ground measurements of Gamma rays from thunderclouds were
performed by Brunetti et al. (2000). They've used a scintillation detector based
on a NaI(TI) monocrystal shielded on the sides and bottom by 1 cm Pb
(Plumbum), 0.2mm Cu (Copper), and 0.3 Al (Aluminum).
For the entire observation period they have maintained the integral counting
rate per minute in the range from 400 keV up to the detector’s end and the
counts per hour in two energy bands: 0.1-2.8 MeV (Environmental Radiation,
ER) and 3-10 MeV (Cosmic Rays exclusively, CR). The ratemeter, measuring
the radiation percentage count difference was 20% above the average level
during the events.
The histograms of the integral counts showed that the ER was also higher than
the average while the CR remained approximately constant, with the exception
of a significant increase in the peak hour, which varied among the
measurements, but was clear in the measurement of June 11th of 1996 between
1:00 and 2:00 a.m.. The slow increase in the gamma radiation was attributed to
the radioactive aerosol transported to the ground by the rain. And the fast
increments of gamma ray up to 10 MeV were attributed to bremsstrahlung
radiation from high energy electrons accelerated by strong thunderstorm electric
fields.
In 2002 Torii et al. (2002) reported measurements of increases in the
environmental gamma-ray dosage at least four times during the previous five
years at the Monju site, a nuclear power plant facing the Japanese sea. The
24
largest increase was on January 29, 1997. They have used Environmental
Radiation Monitors (ERMs). These augmentations lasted several tenths of
seconds, as shown in Figure 2.9, and originated from a thundercloud in the
Monju site vicinity. They used thermoluminescent dosimeters, which indicate an
increase of 0.1mGy (1 mGy = 1 mJ/kg). The spectrum measured by a NaI(Tl)
(Sodium iodade doped with Thallium) scintillations detector was continuous,
reaching several MeV.
Figure 2.9 - Dose enhancement during thunderstorm measured by ERMs.
Source: Torii et al. (2002).
These augmentations were recorded only in association with winter
thunderstorms. Torii et al. (2002) suggested that this was due the lower cloud
base during the winter, as low as several hundred meters, such that the photon
sources would be at a low altitude. If the source was at several kilometers the
dose increase would be difficult to measure because of attenuation.
Since the photon spectrum seems to be consistent with bremsstrahlung
emissions from energetic electrons, Torii et al.(2002) simulated energetic
electrons in the thunderstorm electric field using the open software, Electron
Gamma-ray Shower 4 – EGS4 , a Monte Carlo code that includes the main
interactions between photons and matter. In the simulations, the authors
assumed: (1) a uniform electric field from the ground to 1 km altitude with
magnitude of 100-280 kV per meter; (2) constant air density of 1.293 kg per
25
cubic meter; and (3) one million seed electrons starting from 1 km of altitude
with 5 MeV of initial energy. Following these assumptions, they calculated the
photon energy spectra showing that the number of photons increases with the
electric field (Figure 2.10). Comparing the simulation results with the dose
enhancement measurements, Torii et al. (2002) concluded that the acceleration
of energetic electrons and the subsequent bremsstrahlung emissions were the
cause of the dose enhancements observed.
Figure 2.10 - Calculated photon spectra on the ground with different electric
fields.
Source: Torii et al.(2002).
The next significant contribution in this field was performed by Dwyer et
al.(2004), who reported intense gamma ray and X-ray associated with rocket-
triggered lightning. They used two instrumental setups, 10 meters apart from
each other and both 650 meters away from the mobile rocket launcher of the
international center for lightning research and testing at Camp Blanding Florida.
Both setups used NaI(Tl) scintillators with different dimensions mounted on
photomultipliers tubes. The first setup was 12.7 cm diameter and by 7.6 cm
thick cylinder and was accompanied by one identical control detector with no
scintillator while the second consisted of a 7.6 cm by 7.6 cm cylinder
accompanied by one identical control detector with no NaI. A huge burst of
gamma rays was observed by all NaI detectors in association with the third
26
rocket-trigged lightning discharge. The energy spectrum for the whole event
reached ~ 10 MeV. These measurements confirmed lightning as a source of
these high energy emissions.
Photon energy spectra consistent with bremsstrahlung emission were also
found by Tsuchiya et. al. (2009) that reported observations performed between
September 4, 2008 and October 2, 2008 at the Norikura cosmic ray observatory
at 2770 m altitude in Tokyo, Japan. The observation system consisted of a
spherical NaI scintillator and a plastic scintillator enclosed in an aluminum box
both with time resolution of one second, each one with a photomultiplier of its
own. The NaI scintillator covered the range of 10 keV- 12 MeV while the plastic
scintillator operated with a threshold energy deposit of 500 keV.
Tsuchiya et al. (2009) reported an event on September 2008 in which they
found a long-duration gamma ray flux enhancement during thunderstorms. They
also performed simulations of the ground propagation of gamma ray photons
using the COsmic Ray SImulations for KAscade – CORSIKA and EGS4, both
Monte Carlo codes. They estimated the spectrum observed on ground from a
source photon spectrum with distances up to 1 km. The simulated spectrum
followed a power law, and they interpreted their results based on the relativistic
runaway mechanism.
Tsuchiya et al.( 2011) reported long duration gamma ray emissions extending to
10 MeV and lasting longer than 1 minute, during the Gamma-Ray Observation
of Winter Thunderclouds experiment (GROWTH) in Japan. GROWTH works
with two separated systems on the roof of a nuclear power plant in Niigata, 40
m above sea level. One system used two NaI scintillators shielded from natural
low energy radiation by BGO scintillators, causing the system to avoid
surrounding radiation and have preferential detection sensibility on the radiation
coming from the sky direction. The system operated in the energy range from
40 keV up to 10 MeV. The second system consisted of spherical NaI(Tl) and
CsI(Tl) (Cesium iodide doped with Thalium) scintillators, covering a higher
energy range, 300 keV – 80 MeV, and it was set up 10 meters apart from the
first system. This last one remained unshielded causing them to have an
omnidirectional detection and therefore detecting the surrounding radiation.
27
Completing the experimental setup, they used three optical sensors and an
electric field mill as environmental monitors.
Tsuchiya et al. (2011) simulated the photon spectrum using CORSIKA and
EGS4 assuming power law bremsstrahlung emissions, and the source heights
were estimate to be 290-560 m and 120-690 m, at 90% confidence level. The
number of energetic electrons that produced these prolonged gamma ray
emissions was estimated in 109-1011.
Gamma-ray events associated with thunderstorms were also reported by
Chilingarian et al.(2012a). Detectors at the facilities of the Aragats Space
Environment Center (ASEC), Armenia, measured 243 events composed by
charged and neutral particles flux of secondary cosmic rays which is a resultant
cascade of the interaction between the cosmic ray and atmospheric particles.
On May, 2011 Chilingarian et al. (2012a) detected a large and abrupt
enhancement of particle count rates correlated with thunderstorm activity, which
were named Terrestrial Gamma-ray Enhancements (TGEs). They had low
amplitude and long duration (~10 min), and constituted less than 10%
enhancement in the gamma-ray signal of the secondary cosmic-ray emissions.
The event was accompanied by an abrupt increase of the near surface electric
field caused by a –CG and then the TGE started. The peak gamma-ray intensity
was 70% above the background when the electric field was minimum.
Chilingarian et al.(2012a) suggested that the RREA process could not generate
these low amplitude emissions as there was no lightning occurrence in some
measurements and RREA process would not start. Chilingarian et al.(2012a)
also performed simulations using the Monte Carlo code , GEANT4, to estimate
the energy spectra of these events using a uniform electric field of 1.8 kV/cm
from 3.6 km to 5 km to accelerate the particles. They used a wide energy range,
1-300 MeV, for seed electrons. They proposed then a simultaneous process to
generate the most energetic particles, the Modification Of energy Spectra
(MOS) process that consists in the modification of secondary cosmic ray
particle spectrum which would be responsible for these low amplitude TGFs. In
order to compare these processes, they ran other simulations with a uniform
electric field with intensity of 1.7 kV/m between 3.4 km and 5 km, above the
28
RREA critical energy, and fields below this value to demonstrate the influence
of the MOS process. The RREA process provided maximum energies for
electrons of 30-40 MeV and for photons of 20-30 MeV while the MOS process
was able to accelerate electrons up to 60-70 MeV and 80-90 MeV for gamma-
ray photons.
Even though these events are different from TGFs, because of the long duration
registered by Chilingarian et al.(2012a), they are also possible sources of
neutrons. Chilingarian et al.(2012a) correlated these events with the generation
of charged layers in the thunderstorm because of their duration, 10 minutes,
and they registered hours of their occurrence that match the related phases of
the storm.
2.4. Simulations of gamma rays related with atmospheric processes
In order to analyze the BATSE and RHESSI data, Dwyer et al.(2005) performed
Monte Carlo simulations of runaway breakdown comparing the energy spectra
both from BATSE and RHESSI. They also performed an altitude estimation of
the phenomena by simulating different atmospheric depths using four values of
reduced electric field (electric field divided by the air density), which were 300,
400, 1000 and 2500 kV/m. With all the relevant photon interactions with matter
taken into account, i.e. excitation, Møller scattering and elastic scattering. The
Bremsstrahlung processes were also fully modeled as well as Compton
scattering, pair production, photoelectric absorption and pair annihilation. As a
result, they found that the simulated spectrum with an atmospheric depth of 50
g/cm2 and an electric field of 400 kV/m at STP closely matches with RHESSI
spectrum. The source height was estimated at 21 km, implying that the TGF
source is not the Sprite discharge.
One of the possible TGF sources is the lightning leader. Assuming that, Carlson
et al.(2010a) created a TGF model focusing on the electric field near the leader
channels and then inject seed electrons into the electric field to start the
avalanche process via RREA, using GEANT4 Monte Carlo simulations for of
RREA and bremsstrahlung processes for the gamma ray emissions. The
electric field was calculated using an integral equation that took into account the
29
geometry, charge density and current density of the channel. This integral was
evaluated using the thin wire approximation with the electric field limited to 10
MV/m electric field value at sea level. For the initial conditions, they used
uniform downward electric ambient field, lightning channel length of 100m -3 km
and its upper tip on 0-20 km above the sea level, the seed particles had 200
keV of initial energy.
Carlson et al. (2010a) produced a spectrum with a peak at 16 MeV with a broad
distribution in good agreement with TGF observations. The duration of the
pulses generated were shorter than the observations, and according to the
authors, this feature was due the static nature of the channel they have
simulated.
Their model showed that higher peak currents on the channel and low altitude
channels tended to generate stronger TGFs. The results allowed imposing
threshold in the magnitude of the lightning current capable of producing a TGF,
since maximum photon energies exceed 40 MeV for current pulses amplitude
above 100 kA.
In the view of the astonishing observations performed by the AGILE team
(TAVANI et al.2011), Celestin et al.(2012) performed Monte Carlo simulations of
thermal runaway electrons accelerated in a very strong inhomogeneous electric
field of lightning discharge at the leader head. They showed that the resulting
bremsstrahlung spectrum reproduced these recent observations.
Celestin et al.(2012) assumed that the atmosphere was composed by 80%
nitrogen gas and 20% oxygen. They considered only ionization and elastic
scattering for electrons, due to the worked energy range of 104 - 2x108 eV they
assumed for the electrons. They introduced a continuous radiative friction of
electrons due to the bremsstrahlung. They established that the TGF source had
a broad beam with 45 degree angle at 15 km altitude. Celestin et al.(2012)
tracked photons until 500 km altitude and notice that no collision was likely to
occur between photons and air molecules after 100 km altitude, considering the
processes that they have taken into account, i.e. photoelectric absorption,
Compton scattering and pair-production. The model developed by Celestin et al.
(2012) reproduced the high energy TGF spectrum presented by Tavani et al.
30
(2011), while the RREA process was only capable of fitting TGF spectra with
energies up to 30 MeV.
Köhn (2014) simulated electrons accelerated by a negative lightning leader at
the moment of stepping, analyzing the production of positrons, neutrons and
protons for gamma ray emissions from the stepping leader. He used a vertical
4 km long leader geometry with 1 cm tip radius, the leader was considered to be
equipotential and under the influence of an external electrical field of 0.5 kV/cm.
The leader had a start altitude of 16 km and it was directed upwards. The
electrons had an initial energy of 0.1 eV and their initial position was 30 cm
ahead of the leader tip.
The model developed by Köhn (2014) consists in a three dimensional Monte
Carlo simulation covering relevant processes for each particle type. In Köhn
(2014) the following electron and photon processes were considered: for the
electron, molecular excitations; elastic scattering; impact ionization; attachment;
electron-nucleus and electron-electron bremsstrahlung. The considered photon
processes were photoionization; hadronic production; Compton scattering and
pair production.
An initial photon distribution between 5 and 40 MeV was set at 16 km altitude as
input for Köhn (2014) particle production model. The particle motions were
upward directed. Köhn (2014) presented with his model, a ratio of neutron or
proton production over the positron production, Figure 2.11, and finally a
neutron energy distribution after 14 μs from the simulation start, Figure 2.12.
31
Figure 2.11 - Rate between the neutron and positron production and rate
between the proton and positron production as function of the
photon energy.
Source: Köhn (2014)
Figure 2.12 – Neutron energy distribution after 14 μs of the simulation start.
Source: Köhn (2014).
32
33
3. Atmospheric neutrons
The first observations of neutron emission during a thunderstorm related with
lightning discharges were performed by Shah et al.(1985) at the high altitude
peaks of Gulmarg, India. They estimated a neutron number between 107-1010
per lightning discharge during the observations performed between May 1980
and May 1983. They’ve used a neutron monitor composed by 21 BF3 (Boron
Trifluorete) counters to detect low energy cosmic rays. The background signal
was 1.8x104 neutrons per 30 minutes, due to low energy cosmic rays neutrons,
and the total area was 3x104m². Electric field variations caused by lightning
discharges were registered by a fast linear antenna installed in the monitor’s
vicinity.
The monitor’s detectors opened sequentially for 80 microseconds registering up
to 99 neutrons without saturation. They recorded for a total of 320
microseconds after the arrival of the first neutron emitted by the lightning, which
was identified based on a timer that was triggered by the signal of the antenna.
The time delay between the electric field variations caused by the discharge
and the first neutron detected was used to estimate the distance of the lightning,
considering a line-of-sight propagation. The 320 microseconds reading time is
very large compared with the average duration of lightning, 50 microseconds,
and very short compared to the average time between two consecutive
discharges, 40 ms, which allowed a good estimation of the number of neutrons
per each lightning discharge. These observations did not allow any conclusion
about the production mechanism of these neutrons.
In contrast to the high altitude measurements realized by Shah et al. (1985),
Shyam et al.(1999) performed measurements, in Mumbai, India, at sea level.
They used detectors with sixteen BF3 counters embedded in neutron
thermalizing material and recorded neutron bursts that had up to 109 counts.
The thermalized neutrons undergo in a reaction with B10 (Boron) producing
lithium and helium ions that are detected by the counters. They recorded
neutron bursts in a continuous mode and registered bursts under different
weather conditions, associating the higher bursts during lightning conditions
34
with the discharges. Their results are summarized in Table 3.1 extracted from
Shyam et al. (1999).
Table 3.1 - Summary of Shyam et al.(1999) results.
Source: Shyam et al.(1999)
They estimated a threshold for neutron detection of 4x108/lightning and the
maximum count observed in a burst was 1.4x109. They suggested that the
production mechanism of these particles is nuclear reaction, i.e. fusion,
between protons, deuteriums and other atmospheric gases. But Babich et al.
(2010) analyzed the production mechanism and concluded that the fusion
mechanism is not a possible mechanism for these emissions.
Space born neutron measurements related to thunderstorms were performed by
Bratolyubova-Tsulukidze et al.(2004). They found the most intensive fluxes in
Africa and the Pacific Ocean. They used the Ryabina-2 detecting module on
board the Mir orbital station, Scorpion-1 onboard International Space Station
(ISS) and the Analyzer of Particles and Fields (APF) onboard Kolibri-2000
satellite orbiting with an initial height of 385 km and an inclination of 51.6
degrees. Mir was at an orbit with 51.6 degree inclination between 320-420 km
altitudes, the ISS orbit had 51.6 degree inclination in relation to Earth’s equator
at 400 km altitude.
The Ryabina-2 module consisted of 12 slow neutron helium discharge counters
surrounded by 15- cm coating of an organic moderator. It detected neutrons
within the energy range of 0.25 eV-1.9 MeV, i.e. after they slowed down to
thermal energies, with near 80% efficiency. Scorpion-1 consisted of 2 parallel-
35
connected counters detecting neutrons in the range of 0.1 eV – 1 MeV, and it
did not use a moderator. The APF detector was identical to Scorpion-1.
The background increases were analyzed and in all three experiments
simultaneous neutrons and galactic cosmic rays protons with energies more
than 50 MeV were registered, as well as neutron bursts with energies between
0.1 eV and 1 MeV. Figure 3.1 shows a comparison of the spatial distribution of
the events with the lightning distribution measured by OTD. The first row shows
the OTD data, the second shows the high background neutron fluxes detected
by Mir and the third shows the neutron bursts detect by Kolibri-2000. Assuming
a detection altitude of 400 km, Bratolyubova-Tsulukidze et al.(2004) associated
the events with lightning discharges and estimate a production of 1010 neutrons
per lightning.
Figure 3.1 - Upper panel, OTD lightning map. Middle panel, Mir's neutron flux
measurements. Lower panel, Kolibri measurements.
Source: Bratolyubova-Tsulukidze et al. (2004).
36
During routine measurements of the background count rate of low energy
neutrons in São José dos Campos (600 m above the sea level) , Brazil, Martin
et al.(2010) registered a sudden and sharp increase in the count rate
simultaneous with a lightning discharge that occurred in the vicinity of the
detector. The detector used was a standard He–3 tube detector capable of
detecting about 80% of the thermal neutrons. The neutron counts were
integrated over 1 minute interval. During the measurements they’ve used an
identical setup without the tube detector to be able to reject false readings and
noise signals.
The detector was located inside a one-floor building with brick walls covered
with clay roof tiles. Measurements in fair weather recorded between 0 and 2
counts per minute while the measurement during a lightning storm had a peak
of 690 counts per minute during an event that lasted 2 minutes. The mean
background count rate before the discharge was 0.75 counts per minute. The
distance between the detector and the discharge was roughly estimated in less
than 0.5 km by seeing the discharge and registering the time lapse to hear the
thunder. With the registered count and the estimated distance, they were able
to also roughly estimate a production of 1012- 1013 neutrons by the lightning
discharge.
Two years later Starodubtsev et al.(2012) reported results of an experiment at
100 m above sea level in Tuimaada Valley, Russia, in which they measured
neutron fluxes of 4x10-3 neutrons/cm2.s. Starodubtsev et al.(2012) used a
cosmic ray spectrograph with 1 minute time resolution consisting of one neutron
monitor They also used four muon telescopes placed in different levels and
measuring the particle intensity coming from five directions: vertical, 30º, 60º,
north and south. A fluxmeter with 1 second resolution with measurement range
of ± 50 kV per meter measuring the electric field and its variations. A fluxgate
magnetometer with half second resolution and range of ± 3200 nT was used to
measure the magnetic field, and a high speed camera was used for lightning
recording, enabling them to determine the discharge characteristics.
The observations were performed from 2009 to 2011; they registered 39
thunderstorms and 9 of them, which were intense thunderstorms, presented
37
significant neutron bursts. Based on the electric field variations they suggested
that the thundercloud had the classical tripolar configuration for all the neutron
bursts recorded. Further analysis revealed that short-term neutron bursts were
detected when the average electric field reached – 16 kV/m, as shown in Figure
3.2. The Figure clearly shows a neutron count highly above the background as
function of the electric field strength of the lightning discharge.
Figure 3.2 - Neutron count versus electric field strength in the presence of
lightning discharges in July 26, 2010. The straight line represents
the count rate before the thunderstorm.
Source: Starodubtsev et al. (2012).
An extraordinary high flux of low-energy neutrons detected during 17
thunderstorms in the summer of 2010 was reported by Gurevich et al.(2012).
Observations were performed at the Tien-Shan mountain Cosmic Ray station,
Russia, at 3340 m above sea level. The detection system consisted of three
thermal neutron detectors based on Helium-2 with efficiency of 60%.
One neutron detector, called “external” was placed in the open air inside a light
plywood housing at 15 m distance from the others. A detector, called “internal”,
was placed inside a room screened from the top by a 2 mm roofing iron ceiling
and a 20 cm carbon layer. The third one, called “underfloor”, was placed under
the floor of the same room and was additionally shielded from the top by a 3 cm
thick layer of rubber, the floor material was 4 cm of wooden. They also used a
38
standard type neutron supermonitor placed inside the same room as the
“internal” detector, this monitor measured the hadronic cosmic ray component
including high energy neutrons. Output pulses from the monitor counters are
registered continuously with 1- minute time resolution. The electric field was
registered by a field-mill with sampling rate of 1000 Hz, and the fast variations
of the electric field were measured by capacitor-type sensors, both installed in
the vicinity of the neutron detector complex. The electric discharges were
registered using two radio-antenna operating in the range of 0.1-30 MHz.
With this experimental setup, they were able to make comparative
measurements as the Figure 3.3 shows. They calculated an additional neutron
flux during thunderstorm reaching extreme values of 3-5x10-2 neutrons/cm2.s
taking into account the minute neutron counting rates registered in
thunderstorm period and the effective sensitive surface of the thermal neutron
detectors
Figure 3.3 - Record of neutron counting rate and the local electric field.
Source: Gurevich et al. (2012).
Gurevich et al. (2012) measurements were analyzed by Tsuchyia (2014)
because of the high flux of low energy neutrons. He simulated a Helium based
39
detector using GEANT4 in order to evaluate its sensibility examining the high
energy (more than 10 MeV) photons contribution to the detection. Tsuchyia
(2014) reported that this type of detector suffers a large gamma ray
contamination that can interfere on the neutron signal when surrounded by thick
material due to the small sensibility to photons with energy larger than 10 MeV,
opening the question about gamma ray contamination on Gurevich et al.(2012)
observations.
Another high altitude experiment was performed by Tsuchiya et al.(2012), they
reported neutron and gamma ray flashes associated with thunderclouds. The
observations were carried out between May and October at Yangbajing (4300
m above sea level) Tibet, China, with a Solar-Neutron Telescope (SNT) and
the Yangbajing Neutron Monitors (YBJNM). The neutron monitors system
consisted of 28 NM64 – type detectors, each NM64 monitor was composed of
a BF3 counter and the solar-neutron telescope consist of nine plastic
scintillations counters and proportional counters around them. In order to
measure electric field variations, two electric field mills were installed in the
vicinity one on the ground and the other on the roof of a central building. For
03:00-7:00 UT on July 22, 2010, both instruments were corrected for
atmospheric pressure variations and the count rates of both instruments clearly
increase around 5 UT and the SNT higher-energy channels appeared to show
count enhancements in coincidence with the above.
From 25 observed thunderstorms, 5 had prolonged count enhancements and
three of those five were clearly seen by the YBJNM or the SNT. The events,
lasted between 10 and 30 minutes, this was the first observation of such long
events. One of them had a clear correlation with the electric field
measurements. Tsuchiya et al.(2012) was able to define burst time as 40 min,
with statistical significance above the background of 2 sigma, for a 40 MeV
burst registered by the SNT channel. The long duration of the burst and the
gradual change on the electric field led them to conclude that the signal was
associated with the electrical field of the thunderclouds and not with individual
lightning discharges.
40
Observations in the Aragats Space Environmental Center, ASEC, at Mt.
Aragats near 3200 m altitude were reported by Chilingarian et al.(2012, b). They
detected numerous gamma-ray events and thunderstorm ground
enhancements that included neutron emissions. They've used a standard
neutron supermonitor (NM-64), Aragats Neutron Monitor (ANM), to register the
high energy neutrons. This instrument detects atmospheric neutrons in a wide
range of energy having lower efficiency for lower energy. It consists of eighteen
proportional BF3 counters type CHM-15, surrounded by a 5 cm of lead producer
that interact with fast neutrons producing about 10 more neutrons with lower
energy, and a 2 cm of polyethylene moderator material to slow down fast
neutrons. In order to detect the thermal atmospheric neutrons, two proportional
counter chambers were installed but without a producer or a moderator.
Completing the experimental set of ASEC, thin and thick plastic scintillators
were used, the thin ones has higher efficiency to detect charged particles while
the thicker ones has focus on neutral particles.
Chilingarian et al. (2012b) reported 12 peak enhancements of the neutron count
rate recorded by the ANM in coincidence with gamma-ray flux enhancements
observed by the ASEC detectors between 2009 and 2010. The neutron count
may be contaminated by decayed negative muons that were captured by the
detector. They estimated different fractions of muons contribution for different
neutron events ranging from 5% - 15%. In addition to the observations,
Chilingarian et al. (2012b) simulated a neutron spectrum that reached a few
MeV using GEANT4 shown in the Figure 3.4 with gamma ray source at 5000 m
and neutron detectors at 3200 m. Their results supported the photonuclear
mechanism and Chilingarian et al.(2012b) did not correlate these neutron burst
events with lightning, since not all TGE events were accompanied by lightning
and their time was minutes.
41
Figure 3.4 - Simulated neutron spectrum using GEANT4.
Source: Chilingarian et al. (2012b).
Using a cosmic ray spectrograph consisting of a neutron monitor and four muon
telescopes, plus an electrostatic fluxmeter and a magnetometer to record the
lightning discharges, Kozlov et al. (2013) observed 14 neutron bursts from
thunderstorms. The data from 51 thunderstorms within a 10 km radius from
Yakutsk were recorded in 2009-2012. The 24 counters showed an average
count rate of 16500 counts per minute. Different field variations were associated
with different charge configurations in the cloud, all the burst were observed
with a field variation that indicate a cloud following the classical tripolar
approximation. Almost all the bursts were observed during negative discharges
from a thunderstorm on June 14, 2012, there were a few neutron bursts
associated with positive discharges.
Neutrons bursts correlated with negative lightning discharges were reported by
Toropov et al.(2013). The events were recorded by the Yakutsk cosmic ray
spectrograph, 105 m above the sea level. Figure 3.5 shows one of the events.
In some events the counting rate increased by 21% above the background
(2688 neutrons per minute). The instrumental setup consists of the standard
neutron monitor and two electric field sensors, one installed in the vicinity of the
neutron monitor and the other 4 km apart from the monitor allowing them to
detect discharges in a radius of 10-15 km with one second time resolution. Two
storms were recorded in high-speed video.
42
Figure 3.5 - Neutron burst and lightning correlation. The first panel shows the
neutron count and the second panel shows the electric field
variations in temporal coincidence with the neutron detection.
Source: Toropov et al. (2013).
During the observation period 2009-2011 the neutron monitor detected bursts
during lightning discharges. During the summer seasons 39 thunderstorms
were recorded in the vicinity of the neutron monitor, in nine of them the neutron
flux level was high. All the observations of bursts in the neutron component
were interpreted as being correlated with a tripolar charge structure of
thunderstorm cloud. The bursts were observed in the second half of the
thunderstorms lifetime, just after the compact positive charge center had
passed over the observation point.
In the thunderstorm observed on June 11, 2011, the cloud-to-ground negative
discharges caused an increase in the neutron flux. In that particular storm the
distance between the monitor and the strike was in 5.8-7.1 km. All the
discharges on June 11, 2011, which were accompanied by bursts in the neutron
component, struck the top of the terrace or the terrain slope. In these cases the
points of strikes were high enough to fall within the line of sight of the monitor.
All the peaks in the neutron component occurred during the nearby
thunderstorms in, which the cloud had a certain tripolar charge configuration,
although not all the clouds with that configuration had a neutron component
response, only 9 of 16 of the thunderstorm with tripolar charge distribution were
accompanied by neutron bursts. No differences were found between the
43
thunderstorms that caused bursts and those that did not, thus Toropov et
al.(2013) suggested that an additional factor may affects either the generation
of neutrons in the lightning channel or the registration of the emitted neutrons.
Agafonov et al.(2013) reported, for the first time, neutron emissions with
energies between 0.01 eV- 10 MeV related with electric discharges. They
registered the emissions during the initial stages of the discharges together with
X-ray emissions using plastic scintillators to register the neutrons and POPOP
scintillators of polystyrene to detect the X-rays. The experiment consists of a
beam of electrons accelerated by 1 MV, in order to produce electrical
discharges in the air with 10 kA – 15 kA with 1 meter length. In order to detect
the neutrons, Agafonov et al.(2013) used a CR-39 detector, which was not
sensitive to electromagnetic radiation. The detection of the thermal neutrons
was performed through the count of paths of alpha particles with at least 2 MeV
energy produced by the neutrons in reaction with the boron of the detector and
the fast neutrons with 10 MeV or more were registered by the observation of 3
alpha particle generated in a reaction with carbon and exiting from the same
position.
3.1. Simulations of neutrons related with atmospheric processes
Malyshkin et al.(2010) developed simulations of neutron propagation through
the atmosphere up to orbital altitudes in order to compare the observations of
Bratolyubova-Tsulukidze et al.(2004). Their results suggested that it is unlikely
that these space born observations are connected with TGF phenomena. They
used GEANT4 to simulate the particles propagation in order to estimate the
possibility to obtain the neutron flux on orbital altitudes generated by
photonuclear reactions.
Malyshkin et al. (2010) used atmospheric parameter extracted from MSIS-90
model and initial 108 neutron histories, i.e. primary particles, simulated in an
isotropic distribution. In order to compare the simulation with the orbital data,
Malyshkin et al. (2010) recalculated the Kolibri-2000 data using 30 km as the
initial altitude and 1015 initial neutrons. With these parameters, count rate was
0.5 per second, in general agreement with the experimental data.
44
Malyshkin et al.(2010) used a point photon source with initial directions
distributed in a 20 degree half-angle cone and initial energy in the range of 10-
20 MeV with a spectrum proportional to E-1. 107 initial photons were set at
several initial altitudes as 30, 40, 50, 60 km with all the relevant interactions with
air molecules. Finally reaching the resulted neutrons, with shown spectrum in
the Figure 3.6, which reach the orbital altitudes, 500 km, in a 0.1 per second
rate in the best case scenario with a source in 30 km while the background
count of the Kolibri-2000 was 0.1-0.2 count per second.
Figure 3.6 - Energy neutron spectra on 30 km altitude (continuous line), and on
500 km (dashed line).
Source: Malyshkin et al. (2010).
In the view of the several observations of thunderstorm related neutron
emissions on the ground, Babich et al.(2010) simulated neutron generation and
propagation from several source altitudes in an attempt to estimate the source
altitude, assuming that the neutron production was via photonuclear reactions
and using the universal spectrum of bremsstrahlung from relativistic electron
avalanches described on previous works. The initial neutron energy spectrum
they obtained is shown in Figure 3.7.
45
Figure 3.7 - Simulated neutron energy spectrum on the source altitude.
Source: Babich et al.(2010).
The simulations were based on Monte Carlo technique with a photon energy
threshold of 10.5 MeV, which is the energy necessary to the photonuclear
reaction, the processes of photon interaction considered were Compton
scattering, production of electron-positron pairs and the photonuclear reactions.
Since high energy photons produce particles with approximately the same
direction, one dimension simulations were performed and result in a production
of 4.3x10-3 neutron per photon with the used photon spectrum. The atmosphere
was considered to be composed of a mixture of 80% nitrogen and 20% oxygen
and neutron underwent elastic and inelastic collisions and capture. For neutron
simulations, a detector in several heights was simulated following the different
detectors size of observational experiments.
Exploring the idea of neutrons production by TGFs via photonuclear reactions
Carlson et al.(2010b) simulated the production of 1012 neutrons per TGF with a
source photon spectrum with energies up to 20 MeV. The dominant process for
nitrogen, photoneutron production, of N14 reaction occurs for photons with
energy greater than 10.55 MeV and an energy dependent cross-section that
reach a large peak, of 14 millibarns (1 millibarn is equal to 10-31 m²) at 23 MeV.
In comparison, the pair production and Compton scattering are approximately
170 millibarns so the photonuclear cross section represents only 5% at most of
total photon interaction for the peak energy.
46
Carlson et al.(2010b) ran the GEANT4 package that covers all relevant
electromagnetic and nuclear interactions as Compton scattering, pair
production, photonuclear production, elastic and inelastic collisions, radiative
capture as well. The initial conditions were chosen to meet the TGF parameters,
and started the simulation from the bremsstrahlung photon spectrum produced
by electrons in an avalanche growth of population of relativistic particles.
Considering a photon spectrum up to 20 MeV which does not cover the whole
photonuclear cross section energy range, only 1% of the photons were above
the energy threshold to produce neutrons. The initial photons were simulated
from several source altitudes with either an isotropic distribution or over a cone
with 20 degree aperture and an atmospheric density profile extracted from the
literature.
The neutrons then produced were tracked and recorded if reach altitudes below
0.5 km or above 350 km. The neutrons were produced mostly by unscattered
photons and their distribution had a mean energy of 3.9 MeV. Figure 3.8 (a)
shows the characteristic spectrum. The black curve is the neutron spectrum at
the production altitude, the black dots represent the neutrons reaching the
ground, and the gray line the ones reaching satellite altitudes. The latter were
often produced far away from the photon source due to the photons mean free
path that is in order of 1 km times exp(z/H) because of the atmospheric density
profile, where z is the altitude and H is the scale height considered of 8 km,
implying that most photonuclear reactions occurred far away from the photon
source. Neutrons that reached the ground travelled in a pulse of 10
microseconds while the ones that reached satellite altitudes were in a pulse of
50 milliseconds. Carlson et al.(2010b) also simulated an isotropic source of
neutrons, represented in the Figure 3.8 (b). The Figure also shows the neutrons
produced by the photon source.
47
Figure 3.8 - (a) Simulated neutron energy spectra. The black line is at the
moment of neutron's creation, the black dots are the neutrons
reaching the ground and the gray line are the ones reaching
satellite altitudes. (b) Dispersion of simulated neutrons in a 20
degree aperture cone, in gray, and isotropically, in black.
Source: Carlson et al. (2010b).
Studying the radiation environment at aircraft altitudes, Drozdov et al.(2013)
performed simulations of thunderstorm neutron flashes in the low atmosphere
altitudes, below 10 km. They’ve used GEANT4 and an atmospheric profile
provided by the online MSIS-90. For the TGF event, they considered a point
gamma ray source with spectrum calculated using the RREA bremsstrahlung
generation (DROZDOV et al. 2013). They used 10 – 30 MeV photons and
considered using emissions upward, downwards in a 90 degree solid cone and
isotropic. The source was placed at in 10, 15, 20 km initial altitude with 1017
photons. Figure 3.9 shows an example of the neutron fluxes generated by the
gamma-rays. According with Drozdov et al.(2013) results, thunderstorm neutron
flashes may be a considerable dose for individuals onboard an aircraft as the
emitted particles diffuse in the atmosphere. However, since the events are
considered rare, they concluded that neutrons may be considered a meaningful
dose only to air crew members.
48
Figure 3.9 - Simulated neutron energy spectrum.
Source: Drozdov et al. (2013).
The information on neutrons simulations and observations are summarized in
Table 3.2 which includes the neutron production, observation time and the
analyzed energy range as well as the resultant distribution, estimated source
altitude and the distance between the detectors and the source.
49
Table 3.2 - Observations and simulations results and characteristics summary.
Works Production
[per event]
Observation
time
Registration
[per minute]
Energy [Mev] Source
altitude
Source
distance
Shah et al.
(1985)
107 – 10
10
0.32 s - <2.45 - -
Shyam et
al.(1999)
108 – 10
9
Continuously - - - -
Martin et
al.(2010)
1012
– 1013
Continuously 690 ~0.025 x10-6 - 0.5 km
Tsuchiya et
al. (2012)
- Continuously 1-3x103 1-10 < 5 km -
Gurevich et
al. (2012)
- Continuously 1.8-3x106 < 1 x10
-6; >
~10²
- -
Chilingarian
et al. (2012)
- Continuously ~1336 < 5 5 km -
Starodubtsev
et al. (2012)
- Continuously 16.5x103 > 10 - 1- 3 km
Toropov et
al.(2013)
- Continuously 2688 < 1.65 x103 - 5-7 km
Babich et
al.(2010)
4.3x1012 - - < 20 8 km -
Carlson et
al.(2010b)
3x1011
-
3x1012
- - < 10 15-20 km -
50
51
4. On the probability of neutron production
The dominant process for neutron production is the photonuclear reaction of a
photon with energy between 10 to 30 MeV, which is the range of the major
neutron production cross section, as explained in section 2.1.3. The photon can
either be a primary photon within this energy range, or a secondary photon
generated by a photon of higher energy through other interactions.
The energy range considered here for the photons is of 10-100 MeV in order to
take into account the lowest energy photon capable of producing a neutron and
the highest energy measured up to date (TAVANI et al., 2011). In this range,
the dominant interactions for photons are, as described in Chapter 2,
Compton scattering,
pair production,
photoneutron reaction (the photonuclear reaction that releases a
neutron)
and photoproton reaction (the photonuclear reaction that releases a
proton). These are the photon processes considered in this cross section
analysis.
We used analytical expressions for the cross sections of Compton scattering
and pair production from EGS5 (Equations A.1 and A.3), the photoneutron
reaction cross section data from the EXFOR data bank, and the photoproton
reaction cross section from the ENDF-7 data bank. The EXFOR data bank is
available at https://www-nds.iaea.org/exfor/exfor.htm, and the ENDF-7 data
bank is available at https://www-nds.iaea.org/exfor/endf.htm.
The air cross section was estimated by adding the cross sections of each
element multiplied by their concentration:
0.78085𝜎𝑁2+ 0.20950𝜎𝑂2
+ 0.00965𝜎𝐴𝑟 = 𝜎𝑎𝑖𝑟 . (4.1)
52
The numerical data for the photonuclear reactions cross sections were
interpolated using MATLAB function “interp1”. Figure 4.1 shows the cross
sections of photons interacting with dry air.
Figure 4.1 - Cross sections of the dominant photon interactions with dry air. Cs
(blue) is Compton scattering; Pp is pair production; Pn is
photoneutron reaction and Pnp is photoproton reaction.
Photoneutron reactions happen for photons with energy between approximately
10 and 30 MeV, resulting in neutrons with energies between 0 and 20 MeV
because of the binding energy of approximately 10 MeV.
Below 10 MeV the photon does not have enough energy to remove the neutron
from the atom nuclei, and above 30 MeV the photons have exited the energy
range of the Giant Dipole Resonance (GDR), as explained in section 2.1.3. The
probability per collision of primary photons to produce neutrons via
photonuclear reactions was calculated as the rate between the photonuclear
cross section and the total cross section, shown in Equation 4.2
𝑃𝑝(𝐸) =𝜎𝑛(𝐸)
𝜎𝑡(𝐸), (4.2)
Where 𝑃𝑝(𝐸) is the probability as function of the photon energy E; 𝜎𝑛 is the
photonuclear microscopic cross section and 𝜎𝑡 is the total photon microscopic
cross section.
53
Photons with energy above 30 MeV can undergo Compton scattering and pair
production and emit photons within the energy range of photonuclear reactions,
these photons are considered to be secondary. In pair production the photon is
gone, therefore for a neutron to be created this way the produced electron or
positron needs to have enough energy to emit another photon with energy in
the range of neutron production via bremsstrahlung emission. Then this photon
has to engage in a photonuclear reaction. The photoneutron reaction has a
higher probability to happen after a Compton scattering than after pair
production because of the number of processes involved.
The probability of neutron production by secondary photons (𝑃𝑠𝑐) was estimated
considering a single Compton scattering. 𝑃𝑠𝑐 was calculated by integrating,
between 10 and 30 MeV, the differential Compton scattering cross section
multiplied by the photonuclear cross section, and divided by the total photon
cross section. Equation 4.3 shows the probability per collision of a neutron to be
produced by a secondary photon resultant of a Compton scattering as its first
interaction
𝑃𝑠𝑐(𝐸) =∫
𝑑𝜎𝑐(𝐸′,𝐸)
𝑑𝐸′30
10 𝜎𝑛(𝐸′)
𝜎𝑡(𝐸′)𝑑𝐸′
𝜎𝑡(𝐸), (4.3)
where, 𝜎𝑛 is the photoneutron cross section, 𝜎𝑐 is the Compton scattering cross
section, E and E’ are respectively the energy of the primary and the secondary
photon. The integration method was the global adaptive quadrature as
calculated by the MATLAB function “integral”.
Finally, the total probability of neutron production via photonuclear reaction was
estimated by adding the probabilities of neutron creation by primary photons
and secondary photons, shown in Equations 4.4 – 4.5.
𝑃𝑛(𝐸) = 𝑃𝑝(𝐸) + 𝑃𝑠𝑐(𝐸) (4.4)
𝑃𝑛(𝐸) =𝜎𝑛(𝐸)
𝜎𝑡(𝐸) +
∫𝑑𝜎𝑐(𝐸,𝐸′)
𝑑𝐸′30
10 𝜎𝑛(𝐸′)
𝜎𝑡(𝐸′)𝑑𝐸′
𝜎𝑡(𝐸), (4.5)
54
where 𝑃𝑛(𝐸) is the neutron production probability for a photon for a given
photon energy E. There are other minor contributions that are not taken into
account, involving multiple interactions between the first photon collision and
the photoneutron reaction.
The EGS5 cross section expressions used here were checked against with the
cross section set of two other programs, GEANT 4 and the recently written code
of Köhn (2014).
Figure 4.2 shows the comparison for the Compton scattering cross section. The
Figure shows good agreement in the cross section values, except for the region
below 10 MeV. The agreement is expected since this process is already well
studied and has a broad theoretical development.
The data used by Köhn (2014) was available in a data table while the other two
codes have analytical expressions, available in Appendix A, with different
approximations for photon energies above the electron rest energy. Although all
three programs based their cross sections on the Klein-Nishina equation which
is written for Compton scattering by a free electron, the usage of this equation is
valid for Compton scattering by bind electrons if the photon energy is highly
above the electron rest energy of 0.511 MeV because in this range the binding
energy between the electron and the atom's nucleus does not affects in the
cross sections values. GEANT4 uses its own parameterized equation (Equation
A.4). based on Klein-Nishina equation, with the parameters of Table A.1.
55
Figure 4.2 – Compton scattering cross section for EGS5, GEANT4 and Köhn
(2014)
Figure 4.3 in shows the comparison between the EGS5 pair production cross
section and the ones adopted by Köhn (2014) and GEANT4. It shows that the
cross sections are in good agreement for energies above 10 MeV. For energies
below 10 MeV the curves mismatch due to different equations for different
energy regimes, since the energy becomes closer to the electron rest energy,
this makes the comparison below a few MeV unreliable.
Figure 4.3 - Pair production cross section for EGS5, GEANT4 and Köhn (2014).
56
Pair production is an interaction between an incoming photon and a nucleus, so
the cross section for the molecular nitrogen is a factor two bigger than for
atomic nitrogen because there are two nuclei. There is no further effect on the
cross section due the binding energy between the atoms in this case because
the distance between the molecule's nuclei is significantly larger than the nuclei
dimensions, making them two separated targets.
The photon need to have at least the rest energy of the electron and the
positron combined in order to engage in a pair production, therefore, the cross
section values of this process are extremely low for photon energies of a few
MeV. The different approaches among the programs lead to disagreement
between their cross section values in the region of a few MeV.
Since FLUKA program does not provide its cross section set explicitly as the
other programs, it was not included in this comparison.
4.1. Results of cross section analysis
The probability per collision of primary photons to produce neutrons via
photoneutron reactions (Equation 4.2) was estimated for all energy range in
which the photoneutron reaction cross section is not zero and is shown in
Figure 4.4.
57
Figure 4.4 - Probability per collision of primary photons to produce neutrons via
photoneutron reaction as the rate between the photoneutron cross
section and the total photon cross section.
The same rate of Figure 4.4 normalized by the curve integral, Figure 4.5, may
be viewed as an approximation to the neutron spectrum at the source for a
uniform photon spectrum if one subtracts the amount of energy spent in this
reaction to break the nuclear bound energy. The value of 10 MeV was used to
generalize the bound energy of an air molecule, considering the cross section
values taken from ENDF-7, although this value varies between Nitrogen,
Oxygen and Argon respectively as 10.45 MeV, 15.70 MeV and 9.45 MeV
(VARLAMOV, A. et al. 1999). The Figure 4.5 shows that the neutron energy is
between 0-20 MeV with a maximum at ~ 13 MeV, for a uniform photon
spectrum with energy between 10 and 30 MeV.
58
Figure 4.5 - Normalized probability of neutron production plotted against the
incident photon energy Eγ, minus the bound energy Eb.
The probability of a primary photon with energy above 30 MeV to produce a
secondary photon with energy between 10-30 MeV by Compton scattering and
this secondary photon to produce a neutron is much lower than the probability
of a primary photon with energy between 10-30 MeV to create a neutron. Figure
4.6 shows that the probability of production is at least 1.5 orders of magnitude
below probability for the primary photons.
Figure 4.6 - Probability of neutron production by photons with energies above
30 MeV accounting for Compton scattering as first interaction
and subsequent neutron production by the secondary photon.
59
The curve shape in Figure 4.6 is dominated by the Compton scattering cross
section due the integration of the differential Compton scattering cross section
and due the low values of the photonuclear reaction cross section which do not
vary much compared to the values of the Compton scattering cross section.
Figure 4.7 shows the probability of neutron creation estimated through primary
plus secondary processes as a function of photon energy.
Figure 4.7 - Probability of neutron creation as a function of photon energy.
Figure 4.7 shows that the probability of neutron creation by a photonuclear
reaction is concentrated in the 10-30 MeV range. For the neutron production by
secondary photons to be in the order of magnitude of the neutron production by
primary photons the photon source would need to emit more photons with
energy between 30-100 MeV than photons with energy between 10-30 MeV.
But it is shown in the photon spectra related with thunderstorm phenomena,
Tavani et al. (2011) and Celestin et al. (2012), the amount of particle decays as
the energy increases and therefore the amount of neutrons created by
secondary photons is negligible in comparison with the whole neutron
production.
60
61
5. Analysis of the particles’ mean free path
In this part of the work the number of mean free paths the photons undergo
toward the ground, starting at different heights was estimated. The collision
probability per length plays a significant role in the particle production since it is
possible that not all the primary particles engage into a collision. This estimate
provides the fraction of photons that are likely to collide during their motion. The
processes and atmospheric model considered in this analysis follow the
Chapter 4.
The mean free path, as defined in Equation 5.1, is an estimate of the distance
that a particle can travel without interacting,
𝜆 = (𝑛𝜎)−1, (5.1)
where (𝜎) is the microscopical cross section and (𝑛) the number density.
Since the number density is a function of the altitude and the cross section is a
function of energy, the mean free path is a function of both variables (Equation
5.2),
𝜆(𝑧, 𝐸) = (𝑛(𝑧)𝜎(𝐸))−1, (5.2)
where z is the altitude and E is the photon energy. In order to study only its
dependency on altitude (Equations 5.3), the mean free path was integrated in
energy using MATLAB trapezoid method, the “trapz” function,
< 𝜆 > (𝑧) = 𝑛−1(𝑧)1
∆𝐸∫ 𝜎−1(𝐸)𝑑𝐸
𝐸𝑓
𝐸𝑖, (5.3)
where ∆𝐸 is the integrated interval, 𝐸𝑖 is the lower bound and 𝐸𝑓 is the upper
bound of the integral.
Figure 5.1 shows the photon mean free path averaged over energy as function
of altitude. The energy ranges are: 10-15 MeV; 15-20 MeV; 20-25 MeV; 25-30
MeV. The proximity of the plots reflects the small variation of the total photon
cross section. The large variation of the mean free path, from 500 m at 1 km
62
altitude to almost 3 km at altitudes close to 15 km, is due the exponential decay
of the density.
Figure 5.1 - Photon mean free path averaged in energy. Range 1: 10-15 MeV;
Range 2: 15-20 MeV; Range 3: 20-25 MeV and Range 4: 25-30
MeV.
The mean free path multiplied by the mass density permits one to analyze it
independently of the particle position in the atmosphere. The mean free path is
then represented in units of atmospheric depth and dependent only of the
particle energy. It can be defined for each process in g/cm2 as the density in
g/cm3 multiplied by the mean free path, shown in Equations 5.4-5.5,
𝜌 = 𝑀 ⋅ 𝑛, (5.4)
𝜒(𝐸) ≡ 𝜆 ⋅ 𝜌 =𝜌
𝑛𝜎=
𝑀
𝜎(𝐸). (5.5)
where M is the mass in grams of one mol of air molecules, 𝜎 is the process
cross section, 𝜌 is the air density in g/cm-3, 𝜆 is the mean free path, 𝑛 the
number density in cm-3, 𝜒 is the process atmospheric depth and E is the particle
energy. Therefore, if the total cross section is considered, 𝜒 is related with all
possible processes that the particle may undergo and 𝜒 can be interpreted as
the average amount of mass the particle needs to pass in order to interact
through a certain process.
63
The number of mean free paths travelled by the photons was estimated by the
rate between 𝜒 related to the total photon cross section and the integrated
density which they passed.
For an analysis of different energy ranges, an average of 𝜒 at 10-15 MeV; 15-20
MeV; 20-25 MeV; 25-29 MeV was used. These values of 𝜒 were then compared
with the integrated density correspondent to the particle source height from the
ground, following the scale height of Köhn (2014)
𝑁𝑖(𝑧) = ∫ 𝜌0𝑒−𝑧
8.33∙105𝑑𝑧𝑧
0 , (5.6)
𝑁𝑖(𝑧) = 𝜌08.33 ∙ 105(1 − 𝑒−𝑧
8.33∙105 ), (5.7)
where 𝜌0 is the air density at the ground, assumed to be 1.22x10-3 g/cm3, z is
the source altitude and 𝑁𝑖 is the integrated density.
5.1. Results of the mean free path analysis
As the particles move through the atmosphere they can realize a variety of
interactions with the air molecules. Figure 5.2 shows the number of mean free
paths to be travelled by a photon with different initial altitudes. It is clear to see
that although the photons have a high energy, it is very likely that they engage
in a collision, since even from a source altitude of 1 km the photon passes
through at least one mean free path. The probability of a collision to occur if the
particle passes through one mean free path is 63.21% (WOUTER, B. 2005).
64
Figure 5.2 - The number of mean free paths as a function of source altitude, 𝜒𝑡
represents the photons 𝜒 considering the total cross section; and
𝑁𝑖 is the integrated density.
Considering 2-15 km, as the photon altitude sources, the photons have
approximately 3-15 mean free paths to pass through until they arrive at the
ground as shown in Figure 5.2.Therefore, there is a chance of ~ 95%- 99.99%
(WOUTER, B. 2005) for an interaction to occur if the photons travel these
amounts of mean free paths. Taking into account the rate between
photonuclear reaction cross section and the total photon cross section showing
that within the GDR energy range the probability of photoneutron reaction varies
between 0 and 3.2%, a rate of approximately 10-2 neutrons created per primary
gamma photon per energy in the range of 10 – 30 MeV, since the photons
travel long enough to ensure a collision. The probability per collision of neutron
generation may be considered as the probability of neutron production.
Babich et al. (2010) estimated a production rate of 4.3x10-3 neutron per gamma
ray photon. The difference between their estimate and what was estimated in
this work 10-2 neutrons per gamma ray photon for a uniform source photon
spectrum is explained by the photon source spectrum used in their work.
Babich et al. (2010) have used a universal RREA bremsstrahlung spectrum
which have photons with energies up to 20 MeV, therefore, most photons in
Babich et al. (2010) estimate are outside the GDR energy range and do not
count for photoneutron production.
65
Martin et al. (2010) used a point-like neutron source with isotropic diffusion to
estimate the total neutron production. This approach may lead to an unphysical
geometry configuration if the photons are considered to be the neutron source,
since the photons with energy between 10-30 MeV have a mean free path of
between 500 m and 2 km at thundercloud altitudes along the atmosphere and
hence it is more likely that the photons produce the neutrons along all their way
and not at a single point.
66
67
6. Particle Beam widening and EGS5
EGS5 simulations analyze how broad electron and photon beams can become
as they travel from different source altitudes to the ground. The electron beam
has energy between 10-500 MeV so it could produce photons with 100 MeV
and more, while the photon beam energy range is 10-30 MeV to investigate
closely the photons that are able to produce neutrons.
The photon source was assumed to be accelerated electrons; therefore, the
neutron diffusion is a cumulative result from the electron beam diffusion, the
photon beam diffusion and the diffusion of the neutrons themselves on the
atmosphere. The photon and electron motion is simulated with the free
available program Electron Gamma ray Shower 5 (EGS5), which simulate the
particle path through several kinds of material and geometry that can be defined
by the user. The particles were assumed to be monodirectional beams because
the resultant beam widening in this geometry can be extended for all directions
due the isotropy of space, as there is no density changes.
All the user’s definitions and controls on the EGS5 simulation, as well as the
initial conditions, were done by a so called “user’s code”, which includes several
already defined subroutines that connect the user’s code with the whole EGS5
program.
The particle is then discarded if it exits the simulation domain or it reaches a
lower energy threshold defined by the user, 50 keV in the case of this work.
EGS5 holds the following interaction between the photons and the surrounding
air that are relevant in this energy regime:
Compton scattering,
electron-positron pair production, and
multiple Coulomb scattering.
Compton scattering is the most common interaction for photons in the MeV
energy range. EGS 5 assumes that the photon beam is not polarized when
undergoing Compton, Rayleigh and Coulomb scattering. It also has a special
68
treatment for scattering of Linearly Polarized Photons. The charged particles
interactions with the matter supported by EGS5 are:
elastic Coulomb scattering by nuclei,
inelastic scattering by atomic electrons,
positron annihilation, and
bremsstrahlung.
Considering the interactions that EGS5 permit the particles to engage, the
electron and photon beams are able to generate more electrons and photons.
But due the large possible energies of the electron beams, the photons
generated by them can also produce positrons.
In this part of the work, it is simulated separately photon beams and electron
beams. The photon beam with 21x105 photons with a uniform energy spectrum
from 10-30 MeV is simulated to move from 0.3-26 km to the ground, in an
atmosphere without an electric field and their spatial location was recorded after
they travel a distance, defined by the user, in the z axis. A similar treatment is
done for the electrons, but the electron beam starts with 1x105 particles
following the energy distribution given by
𝑃(𝐸) ∝ 𝑒−𝐸
𝐸𝑐 (6.1)
where P is the probability, 𝐸 is the initial electron energy and 𝐸𝑐 is an energy
parameter of 100 MeV to allow high energy values. The energy was limited to
500 MeV in order to avoid infinite values.
The number of particles is chosen to optimize the computer performance, since
those numbers are enough to have a statistical convergence and do not cause
the computer program to take too much time.
The photon energy range is chosen because of the significant values of the
photonuclear reaction cross section and the electron initial energy range was
chosen to be able to produce high energy photons.
69
Since EGS5 does not allow density variation on the simulation, the particles
travel on constant density which is translated to an actual atmosphere by
equivalence of air column density with Equations 6.2 and 6.3. This translation
allows the simulation results to be taken as a vertical beam toward the ground
∫ 𝑛0𝑑𝑧𝑧
0= ∫ 𝑛0𝑒
−𝑧
8.33 [𝑘𝑚]𝑑𝑧𝐻
0, (6.2)
𝐻 = −8.33 [𝑘𝑚]ln (1 −𝑧
8.33 [𝑘𝑚]). (6.3)
where z is the distance travelled in constant density, 𝑛0, and H is the equivalent
height in actual atmosphere. The exponential in equation 6.2 is considered the
atmospheric density decay with height scale of 8.33 km (KÖHN, 2014). In the
Equation 6.3 z = 8.33 km corresponds to an infinite real altitude H. The Table
6.1 shows the correspondence between the distance travelled in constant
density and the actual distance in the atmosphere.
Table 6.1 - Equivalence between distance z travelled at constant air density and
the actual atmospheric altitude H.
z
(km)
0.3 0.5 0.8 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
H
(km)
0.306 0.516 0.841 1.065 2.287 3.719 5.450 7.638 10.612 15.283 26.894
The beam’s aperture angle is calculated by trigonometry. Using the radial
distance from the beam axis, Equation 6.4, and together with the known z
coordinate calculate the angle which is twice the result of Equation 6.5
√𝑥2 + 𝑦2 = 𝑟, (6.4)
𝜃 = tan−1(𝑟
𝑧), (6.5)
where x and y coordinates are of all particles created by the beam that reach z
plane after the motion, r is the radial distance of those particles from the beam
70
axis and the angle is half of the beam aperture. This angle was calculated for
each particle. An arithmetic average is obtained using all product particle of the
beams that reached the ground.
6.1. Beam aperture results
The beam aperture allows one to analyze the particle spatial distribution for
different source altitudes. Figure 6.1 shows the average aperture on the ground
of the photon beams, according to Equation 6.5, initiating at different source
altitudes, translated from the distances used in the simulation according to
Equation 6.3. It is visible that the aperture remains between values of 0-9
degrees. This is due the fact that high energy photons tend to produce particles
with velocities in the same direction of the incident photon.
Figure 6.1 - Average photon beam aperture as a function of the altitude of the
initial beam.
The Figure 6.1 stops at 10.6 km showing that no particles from beams initiating
at higher altitudes reached the ground. Therefore, 10.6 km is an estimate of the
upper limit of the source height of photons detected on the ground.
Figure 6.2 shows the average beam aperture at the ground of an electron beam
with different initial heights. It represents the cumulative widening of the beam
as there is the diffusion not only of the photons generated by the electrons but
also of the electrons themselves, which is indeed higher than the photon beam
but remains below 18 degrees.
71
Figure 6.2 - Average electron beam aperture as function of initial beam altitude.
The Figures 6.3 and 6.4 show the decay in the number of photons reaching the
ground as a function of the initial altitude of each beam. They show that the
photon number decays rapidly, a reason for the large error bars in Figures 6.1
and 6.2.
Figure 6.3 - Number of photons reaching the ground from a photon beam as
function of initial beam altitude.
72
Figure 6.4 - Number of photons reaching the ground from an electron beam
as function of initial beams altitude.
The neutron beam is produced by a photon beam, which in turn is produced by
an electron beam. The results show that the photon and electron beams have a
certain aperture angle which implies that several neutron sources would lie
along the photon beam that diffuse in the air, thus assuming a punctual neutron
source is an oversimplification of the source.
If the electron source would be the tip of a negative stepped leader, the leader
electric field is highly inhomogeneous and with a low range of influence as
stated before in section 2.4, therefore, the electron source can be considered a
series of points. Their emission direction would not be necessarily monodirected
as assumed here in this work and this would be another factor adding for all
particles diffusion in the atmosphere.
73
7. On FLUKA simulations
Simulations in FLUKA were done in order to investigate the neutron ground
detection, estimating the upper limit for a photon source altitude that can
produce detectable neutrons at the ground, the photon and neutron ground
spatial distribution and their energy spectra. These simulations were made with
FLUKA and not with EGS5 because the later program does not hold neutron
motion and production; also because EGS5 does not easily deal with density
variations definitions, such an atmospheric definition is not trivial to be set. On
the other hand, FLUKA output is not flexible as EGS5 and does not provide a
convenient output for the calculation of the beams aperture angle.
FLUKA is a complex tool to simulate the particle interaction with matter; it
covers a broad range of energies from a few keV to hundreds of TeV. The
program does not provide explicit information on how it transports the particles,
and provides several options of how to detect the particles and define the media
through which they travel. Since user-written routines for the FLUKA definitions
are not trivial, only built-in FLUKA routines were used for these simulation.
The photon interactions that FLUKA holds are:
Pair production,
Compton scattering,
Photoelectric effect,
Rayleigh scattering,
Photon polarization,
Photonuclear reactions: Vector Meson Dominance Model; Quasideuteron
interactions; Giant Dipole Resonance (GDR), and
Generation and transport of: Cherenkov, Scintillation and Transition
radiation.
For the current analysis and the treated energy range, the important interactions
are Compton scattering, pair production and GDR. For the neutron interactions
the program allows:
74
Inelastic scattering.
Capture, and
Elastic scattering.
The program allows the user a variety of definitions of the geometry set up,
particle initial conditions and their detection as well. The FLUKA geometry
settings work in a combinatory fashion, i.e., it deals with Boolean expressions in
order to define the regions and media through which the particles travel. For this
work, a cylindrical geometry from ground up to 19 km altitude and 12 km radius
was adopted. The atmospheric density profile was simulated by 76 cylindrical
layers of constant density with 250 m of height. The atmosphere density in
those layers was linearly interpolated by the density of the following array:
[1.2250, 1.1116, 1.0065, 0.9092, 0.8193, 0.7363, 0.6600, 0.5899, 0.5257,
0.4670, 0.4135, 0.3648, 0.3119, 0.2666, 0.2279, 0.1948, 0.1665, 0.1423,
0.1216, 0.0889]x10-3 grams per cm3, given by the 1976 U.S. standard
atmosphere.
The detection occurred on the ground, with ring-shaped detectors, varying radii
from some meters up to 12 km and 1 cm thickness, the circles radii are: 10 m –
100 m, in steps of 10 m; 200 m – 1 km, in steps of 100 m; 1.5 km – 5 km, in
steps of 0.5 km; 6 km – 12 km, in steps of 1 km. This detection fashion was
chosen in order to have a radial symmetry in relation to the source axis and
allow an analysis of the particle radial distance from the source regardless from
their individual position components at the ground. The detectors were filled
with vacuum, so the results can be compared with any physical detectors
considering the input of their efficiency and material characteristics.
Figure 7.1 shows the detectors ring fashion with the radial symmetry from the
starting axis, every two circles define a detector, with the radial symmetry from
the starting axis.
75
Figure 7.1 - Top view of simulation geometry
The simulations consist of four beams of one million photons with energy in the
ranges 10-15 MeV, 15-20 MeV, 20-25 MeV, 25-30 MeV distributed in a uniform
energy spectrum. The beams were downward orientated and started from a
point-like source in the central axis from different altitudes ranging from 100 m -
5 km. The set of studied heights was 100 m, 300 m, 500 m, 700 m, 900 m, 1
km, 1.2 km, 1.4 km, 1.5 km, 1.6 km, 1.8 km, 2 km, 2.5 km, 3.0 km, 3.5 km, 4.0
km, 5.0 km. These heights were chosen because of a greater interest in the
spectra from low altitude sources and because after 3.0 km, a reduction on the
detected neutrons is noted on the ground.
The detection method was the track-length fluence estimator, USRTRACK
FLUKA routine. Therefore, the detectors register a particle through the path
they make inside the detector volume. The thickness was chosen to lower the
chance of double counting. Double counting occurs if a particle travels inside a
detector and exits this detector entering directly into another.
The program output is then the differential distribution of fluence in energy in
number of particles /cm2GeV per incident primary. It displays the neutrons and
photons that arrived at the ground.
The program output divides the recorded photons in a logarithmic energy
binning within the range of 50 keV – 31 MeV. While the neutrons have a fixed
76
treatment by FLUKA, as the detected neutrons have energy below 20 MeV,
they are considered low energy neutrons by the FLUKA with a set of cross
sections based on several data banks, while the neutrons with energy above 20
MeV are treated with calculated cross sections. They are recorded in a fixed
binning of 260 bins in the energy range of 1x10-11 MeV – 20 MeV (FERRARI, A.
et al. 2014).
7.1. Simulation results
Figure 7.2 shows the number of recorded photons as function of the source
altitude while Figure 7.3 shows the same for the recorded neutrons. The particle
number is per primary photon and therefore, the graphs can provide an
estimate of the number of photons at the source for a given particle
measurement of other works.
Figure 7.2 - Photons down to 50 keV per primary photon (between 10 and 30
MeV) on ground as function of source altitude. The inset is a zoom
view of the altitude region 2-5 km.
77
Figure 7.3 - Neutrons per primary photon on ground as function of source
altitude. The inset is a zoom view of the altitude region 2-5 km.
The large number of photons is due the multiplication of particles, i.e., the
primary photons generated more secondary particles, i.e. photons and electrons
that participate in processes of photon production. The low number of neutrons
is due the unlikelihood of photonuclear reactions. In particular, the peak at 0.3
km, on Figure 7.3, indicates that a source located at lower altitude produces
less neutrons due the smaller distance travelled by the photons there are fewer
collisions as the mean free path for photons with the considered energy have
close values for altitudes below 300 m.
The neutron number is in the same order of magnitude for source altitudes up to
2 km that indicates that ground neutron detection is more likely to be related
with a source at altitudes up to 2 km. Although there is also neutron production
at higher altitudes, these neutrons are less likely to arrive at the ground
because as these neutrons travel through the air and collide, they lose energy
and may not be able to travel the required distance to reach the ground.
The spectra shapes remain similar for altitudes up to 1 km, for higher altitudes
one may see a decrease in the high energy peak between 10-30 MeV. Figures
7.4 show photon spectra for different source altitudes.
78
Figure 7.4 - Total photon at the ground with different source heights.
It is important to highlight two different behaviors, the visible decrease on the
recorded photon number for all energies and, in particular, the decrease on the
photon peak between 10-30 MeV as the source altitude increases. The later
feature is due the increase of the available matter for the high energy photons
to interact resulting in the creation of more photons with energy below 0.5 MeV.
The former feature is explained by the increase in the number of photons
absorbed by the atmospheric molecules, at lower source altitudes the source
photons have a higher chance of reaching the ground without energy loss.
Since the original photon beam have energies between 10-30 MeV, the photons
with energy lower than this interval are resultant of interactions with the air.
There is a small peak in ~ 0.5 MeV that may be due to positrons created by the
79
photons with energy above 10 MeV that annihilate with environmental electrons
generating photons with energy 0.511 MeV.
The recorded neutron spectra have significantly lower particle numbers than the
photon spectra as expected. Figure 7.5 shows the neutron number per primary
for different source altitudes.
Figure 7.5 - Total neutron spectra at the ground with different source heights.
The recorded neutrons are in the energy range of ~ 0.01 eV- 20 MeV. For
source altitudes above 3 km, the number of neutrons is significantly lower than
for source altitudes below 3 km indicating that the ground detectable neutrons
are likely to be produced in heights below 3 km with a clear preference for more
energetic neutrons with energy between 0.1 MeV and 20 MeV, which is a
80
consequence of the GDR peak at photon energies between 22 MeV and 25
MeV as shown in Figure 4.4.
Analysis of detectors in different distances from the source axis are displayed in
Figures 7.6-8, where the Figure title subscript indicates the detector number
that recorded the spectrum, thus define the detector location and its surface.
The inner and outer radii of each detector are related in Table 7.1.
81
Figure 7.6 - Photon energy spectra for different detectors with source altitude of
2 km.
Figure 7.7 - Photon energy spectra for different detectors with source altitude of
0.3 km.
82
Figure 7.8 - Neutron energy spectra for different detectors with source altitude
of 2 km and 0.3 km
83
Table 7.1 - Detector radii.
Number of the detector Inner radius [km] Outer radius [km]
10 0.09 0.1
14 0.4 0.5
19 0.9 1
20 1 1.5
21 1.5 2
22 2 2.5
23 2.5 3.0
25 3.5 4.0
Figures 7.6-7 shows the different photon record for distinct distances from the
source axis. For radial distances lower than 1 km there is an increase on the
low energy photon number but for radial distances farther from 1 km the photon
number decreases as a whole. This indicates that high energy photons interact
near the ground producing low energy particles that are incapable of travelling
long distances before hitting the ground, i.e. > 1 km.
Figure 7.8 shows the same analysis for neutrons. Differently from the photons,
the neutron number decreases as a whole, even for the distances close to the
source axis. But, among the close distances, there is a preferential distance of
0.4-0.5 km for the neutron to arrive at the ground since the detector 14 has a
denser spectrum.
Studying how spread the particles are at the ground, Figures 7.9 and 7.10 show
the total of the particles recorded by each ring-shaped detector as a function of
the distance to the source axis. These results allow retrieving the number of
primary photons for a point-like photon source for a given measurement at a
given distance from the source axis, as can be seen further on Table 7.2.
84
Figure 7.9 - Photons per primary photon recorded by different detectors at
different radial distances from the source axis. The different
colors represent the four distinct simulations with different initial
photon energy range.
85
Figure 7.10 - Neutrons per primary photon recorded by different detectors at
different radial distances from the source axis. The different
colors represent the four distinct simulations with different initial
photon energy range.
Figures 7.10 shows it is unlikely that neutrons reach farther than 2 km away
from the source axis. The dominance of the energy ranges 20-25 MeV and 25-
86
30 MeV in the neutron production is clear; this is due to the peak values on the
photonuclear cross section.
The simulations of Babich et al. (2010) and Carlson et al. (2010) used a higher
number of photons to achieve their neutron results than the estimated by
FLUKA simulations presented here. The difference is due the initial conditions
used, Carlson et al. (2010) used a source photon spectrum to match the known
TGFs characteristics at the time, hence theirs spectrum does not cover all GDR
energy range and requires a higher number of primary photons, 3x1011-3x1012,
than the estimate of the present work, 1.5x1011. Similarly, Babich et al. (2010)
have used the RREA universal bremsstrahlung spectrum that also does not
cover all the energy range of the photonuclear reaction, requiring ten times
more photons to produce their simulation results.
The estimated number of primary photons in this work, with energy between
10-30 MeV, to produce the neutron ground register is in the range of 109-1014
establishing bounds for the source photon production. Since the range of the
source photon number is large, there is the possibility of the observation be
result of different events and not only one photon source.
The data summarized in Table 3.2 is used together with FLUKA simulation
results to estimate the number of primary photons required to produce such
observations and the other simulation results.
Since some of the observations, such as Shah et al. (1985) and Tsuchiya et al.
(2012), were done in altitudes highly above sea level, the column density
between the observation and source altitudes is used to estimate what the
source altitude would be for ground measurements allowing the comparison
between the results of those works and the present simulation.
For simplicity, since detector sensitivity descriptions were not found for all
energy range, the detector sensitivity was not taken into account during the
presented estimations. The lack of the sensitivity information makes the
estimated number of primaries a lower threshold for the real photon number
requirement.
87
If an observation reports, as an example, 10 neutrons cm-2 with source altitude
of 2 km, being 1 km horizontally away from the source, the presented FLUKA
results relate 1.8x10-15 neutrons cm-2 per primary, indicating 5.5x1015 primary
photons at the source with energy between 10 and 30 MeV. The estimation is
for a single point-like photon source.
Table 7.2 shows the estimated number of primary photons through the FLUKA
simulations for the observation and simulation works. The neutron observation
does not present an estimate of the number of photons at the source that could
generate the reported detection, therefore, there is no comparison available.
But the simulations reported by Babich et al. (2010) and Carlson et al. (2010)
provided sufficient data for a full comparison.
Table 7.2 - Neutron detection according with the FLUKA simulations with the
observation parameters.
Work Shah
(1985)
Gurevich
(2012)
Chilingarin
(2012)
Tsuchiya
(2012)
Starodubt
sev (2012)
Martin
(2010)
Carlson
(2010)
Babich
(2010)
Detector (1) (2)&(3) (2) (2) (2) (3) X X
ND
[1/cm-2]
1x10-4-
20x10-4
1.8-3 ~ 0.0372 1.4 ~960x10-3 20 3x10-2 1.5x1010
H [km] 5 5 5 5 1-3 2 5 8
Z [km] 2.748 3.34 3.2 3.2 0.1 0.6 0 3
HF [km] 1.6 1 1.2 1.2 2 2 5 3.3
D [km] 0.5 0.5 0.5 0.5 0.5 0.5 X X
PF # 1x109 -
20x109
2x1013 1.86x1011 8.85x1012 4.8x1013 5.7x1014 1.5x1011 1.2x1014
UP # X X X X X X 3x1011
-3x1012
~1015
D [km] 2 1 1 1 1 x x x
PF #
1x1012 -
20x1012
1.8x1014 1.86x1013 7x1014 4.8x1014 X X x
88
In Table 7.2 ND is the “Neutron Detection” reported in each related work; H is
the considered source altitude in each literature data; Z is the observation
altitude for each work; HF is the source altitude considered for the FLUKA
simulations accordingly to the column density equivalence; D is the considered
radial distance, for the calculation of the number of primaries according to the
FLUKA simulations, of the detection from the source axis, two sets of D
distances were used in order to show how the obtained number of primaries
may vary with the distance between the detector and the source axis. PF is the
number of primary photons required for each observation estimated by the
FLUKA simulations under the condition of the flat photon spectrum between 10-
30 MeV used in this work and according with the HF, source altitude, and D,
radial distance, considered; UP is the used number of primary photons in the
other simulations. The detectors (1), (2) and (3) resemble the equipment used
in each observation, being respectively: The Boron triflurote neutron counters
(1); The NM64- Neutron monitors (2); The Helium-3 Thermal Neutron Detectors
(3).
There is a general requirement of the detectors sensitivity description along all
energy range in order to have better estimates on the sources photon number
to generate these observations.
89
8. Discussion and conclusions
Since from thunderclouds altitudes toward the ground the photons with energy
between 10-30 MeV travel several mean free paths, there is a high chance of
collision for every photon. Therefore, considering that all photons interact at
least one time with atmospheric particles, the photoneutron reaction represents
~ 0-3.2% of the photon interactions for individual photon energies. Considering
the uniform photon spectrum covering the energy range of 10-30 MeV, the rate
between the total photon cross section and the photoneutron cross section
indicates that 1% of the photon interactions within this energy range are neutron
creation. A rate of approximately 10-2 of neutrons created per gamma ray
photon, for each energy within the range of interest, was estimated.
The photons with energy above the photonuclear reaction range have a smaller
chance of producing neutrons due the necessary chain of reactions they have
to go through in order to have the required energy for the photonuclear process.
The probability of a photon with energy between 30-100 MeV engage in the
chain process to produce a neutron is less than 0.12%, as shown in Figure 4.7.
Hence, those high energy photons cannot be responsible for a neutron number
excess unless they produce a significantly high number of secondary photons in
the photonuclear reaction energy range.
The neutron detection simulated with FLUKA resulted in a rate of neutron
detected on the ground per primary photon ranging from ~ 10-4-10-2( Figure 7.3)
depending on the photon source altitude. For a photon source at 300 m there is
a peak of neutron detection of ~ 0.01 per primary.
The results also agree with the neutron energy range. In the FLUKA
simulations the neutrons were in the energy range of 0-20 MeV following the
cross sections analysis. It is also observed the dominance of neutrons with
energy between 10-15 MeV in agreement with expected peak, 3.2%, of neutron
production shown in Chapter 4.
90
The photons travel in a beam of finite aperture and the large aperture angle of
the photon beam was estimated in, 2-6º ± 2° degrees. Since there is no
particular reason for all the photonuclear reactions to occur in one point as the
photon mean free path for energies between 10-30 MeV vary from 500 meters
to 3 km between the considered altitudes, a better approximation for the
neutron source is a line geometry, for example. Considering the photon source
to be high energy electrons, the diffusion of both particle beams need to be
combined. This chain process induces a larger aperture angle, 11-13º ±
3°degrees. Considering this whole chain process, cone geometry is a better
approximation than a neutron point source used among the literature.
For an average photon beam, with energy between 10 and 30 MeV, aperture is
2-6º ± 2° degrees according to the simulations done in EGS5. This aperture
angle, together with a source altitude of 5 km, would indicate an average
distance from the source axis of ~ 350 m. The distance is within the radial
distance of 1.5 km a photon beam reaches with a source altitude of 5 km, as
estimated by the simulations on FLUKA .
The FLUKA simulations were performed to simulate the neutron detection on
the ground for different source altitudes. They show that the particle number on
the ground decreases rapidly with increasing photon source height. This
decrease indicates that ground detectable neutrons are created by photons with
source altitude of 5 km at most in order to have a significant particle number at
the ground. The results also show that the neutrons are unlikely to reach radial
distances beyond 2 km from the source axis and are concentrated in the source
axis vicinity, i.e., distances < 0.5 km.
One possibility to distinguish the different type of sources is to have temporal
resolution on the studies to come. In that way, it can be analyzed by the time
scale of the observation if the photon source is the thunderstorm, lightning
discharges or cosmic ray showers.
For photon source altitudes below 2 km, the neutron number at ground is larger
than 0.001 per primary, reaching almost 0.01 for 0.3 km of source altitude as
shown in Figure 7.3. This indicates that for sufficient low photon sources
91
altitudes, almost all created neutrons reach the ground since the detected
neutrons are in the same order of magnitude of the produced neutrons
estimated by the cross section analysis considering a uniform spectrum
between the energies 10 and 30 MeV.
As a final remark, the photon number estimated with the FLUKA simulations for
most observations lies between 1014-1016 primary photons in the photonuclear
reactions energy range. Such large photon number is comparable with the total
photon number created in a TGF estimated by CARLSON et al. 2010b. But,
since the significant photons are only those in the small energy window of 10-30
MeV, the energy range of the photonuclear reactions, only a small fraction of
the total photon number created in a TGF could be the source of neutrons,
which implies that the source of the ground detected neutrons is still unknown.
92
93
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101
APPENDIX A – EGS5 and GEANT4 cross section equations
In this appendix the cross section equations for Compton scattering and pair
production are shown and explained. Equation A.1 shows the expression used
by EGS5 for the Compton scattering differential cross section,
𝑑Σcompt(𝜀,ε′)
𝑑𝜀′=
𝑋0𝑛𝜋𝑟𝑒2𝑚𝑐2
𝜀2 [(((𝜀/mc2)−2
ε′ 𝜀⁄+ 1 −
2(1+(𝜀/mc2))
(𝜀/mc2)2 ) (ε′
𝜀)⁄ +
(1+2 (𝜀/mc2))
(𝜀/mc2)2 +
(ε′
𝜀))] , (A.1)
in which 𝑋0 is the radiation length, a characteristic distance that represents the
particle energy decay in 1/e; 𝑛 is the electron density (electrons per cm³); 𝑟𝑒 is
the classical electron radius; m is the electron mass, c is the speed of light in
the vacuum incident photon energy and ’ is the emitted photon energy.
Equation A.1 represents the differential macroscopic Compton scattering cross
section and has information about the medium by which the photon is going
through. Dividing the expression by 𝑋0 and 𝑛, the differential microscopic cross
section is achieved, since these are the quantities that characterize the medium
on the equation. Further, the differential microscopic cross section is integrated
in 휀′ between the bounds mc2 and 휀 resulting in the Compton scattering cross
section. Equation A.2, based on Koch et al. (1969) (HIRAYAMA et al. (2005)),
shows the expression for pair production differential cross section:
𝑑𝜎𝑝𝑎𝑖𝑟(𝐸+,𝐸−)
𝑑𝐸+=
𝑟𝑒2𝛼𝑍(𝑍+𝜉(𝑍))
𝜀3{(𝐸+
2 + 𝐸−2) [𝜙1(𝛿) −
4
3ln(𝑍) − (4𝑓𝑐(𝑍), 𝑖𝑓 휀 > 50] +
2
3𝐸+𝐸− [𝜙2(𝛿) −
4
3ln(𝑍) − (4𝑓𝑐(𝑍), 𝑖𝑓 휀 > 50]} , (A.2)
Where 𝜉(𝑍) =ln (1194𝑍−2 3⁄ )
ln(184.15𝑍−1 3⁄ )−𝑓𝑐(𝑍) (A.3)
𝑓𝑐(𝑍) = (𝛼𝑍)2((1 + (𝛼𝑍)2)−1 + 0.20206 − 0.0369(𝛼𝑍)2 + 0.0083(𝛼𝑍)4 − 0.002(𝛼𝑍)6)(A.4)
𝜙1(𝛿) = 20.867 − 3.242𝛿 + 0.625𝛿2, 𝑖𝑓 𝛿 ≤ 1 (A.5)
𝜙2(𝛿) = 20.029 − 1.930𝛿 + 0.086𝛿2, 𝑖𝑓 𝛿 ≤ 1 (A.6)
102
𝜙1(𝛿) = 21.12 − 4.184 ln(𝛿 + 0.952) , 𝑖𝑓 𝛿 > 1 (A.7)
𝜙2(𝛿) = 𝜙1(𝛿), 𝑖𝑓 𝛿 > 1 (A.8)
𝛿 = 136𝑍−1 3⁄ (𝜀𝑚𝑒
𝐸+𝐸−) (A.9)
In Equations A.2-A.9, Z is the atomic number of a given element; is the fine-
structure constant; is the emitted positron energy and is the emitted
electron energy and is the electron rest energy. Equation A.2 is integrated
in between the bounds of 𝑚𝑒 and resulting in the pair production cross
section. Further explanation in the equations terms can be found in the EGS5
manual (HIRAYAMA et al. 2005).
Table A.1 describe the parameters used by GEANT4 in its Compton scattering
cross section, Equation A.14.
Table A.1 - GEANT4 Compton scattering parameters.
D e f
1 2.7965E-29 1.9756E-33 -3.9178E-35
2 -1.8300E-29 -1.0205E-30 6.8241E-33
3 6.7527E-28 -7.3913E-30 6.0480E-33
4 -1.9798E-27 2.7079E-30 3.0274E-32
𝜎(𝐸, 𝑍) = 𝑃1(𝑍) (ln(𝐸 𝑚𝑒⁄ )
𝐸 𝑚𝑒⁄) +
𝑃2(𝑍)+𝑃3(𝑍)𝐸 𝑚𝑒⁄ + 𝑃4(𝑍)(𝐸 𝑚𝑒⁄ )2
1+𝑎𝐸 𝑚𝑒⁄ +𝑏(𝐸 𝑚𝑒⁄ )2+𝑐(𝐸 𝑚𝑒⁄ )3 (A.14)
𝑃𝑖(𝑍) = 𝑍(𝑑𝑖 + 𝑒𝑖𝑍 + 𝑓𝑖𝑍2) (A.15)
E E
em
E
103
In the Equations A.14-A.15, a = 20.0; b = 230.0; c = 440.0. E is the incident
photon energy, Z is the atomic number and 𝑚𝑒 is the electron rest energy.
Futher explanation on the parameters can be found on GEANT4 manual and
the expression is available on GEANT4 source code available at
https://geant4.web.cern.ch/geant4/.
GEANT4 uses parameterized Equation A.16 with the parameters of Table A.2
based on the theory of Bethe and Heitler in which Köhn (2014) also based his
cross sections.
Table A.2 - GEANT4 pair production parameters
0 1 2 3 4 5
a 8.7842E-32 -1.9625E-31 1.2949E-31 -2.0028E-32 1.2575E-33 -2.8333E-35
b -1.0342E-33 1.7692E-33 -8.2381E-34 1.3063E-34 -9.081E-36 2.3586E-37
c -4.5263E-32 1.1161E-31 -8.6749E-32 2.1773E-32 -2.0467E-33 6.5372E-35
𝜎(𝐸, 𝑍) = (𝑍 + 1)(𝐹𝑎(𝐸)𝑍 + 𝐹𝑏(𝐸)𝑍2 + 𝐹𝑐(𝐸)), (A.16)
where 𝐹𝑥(𝐸) = 𝑥0 + 𝑥1 ln (𝐸
𝑚𝑒) + 𝑥2(ln (
𝐸
𝑚𝑒))2 + 𝑥3(ln (
𝐸
𝑚𝑒))3 + 𝑥4(ln (
𝐸
𝑚𝑒))4 +
𝑥5(ln (𝐸
𝑚𝑒))5 . (A.17)
Equations A.16 and A.17 follow the same notation than Equations A.14 and
A.15.
